tag:blogger.com,1999:blog-1050326564532544980.comments2024-03-18T22:43:04.854-04:00NumberADayMathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.comBlogger135125tag:blogger.com,1999:blog-1050326564532544980.post-65124987224378309922014-09-20T18:57:02.536-04:002014-09-20T18:57:02.536-04:00There's a slight error (typo) in the definitio...There's a slight error (typo) in the definition of Ackermann function:<br /><br />3rd part should be:<br />"A(x-1,A(x,y-1)) otherwise"<br />and not:<br />"A(x-1),A(x,y-1) otherwise"Anonymoushttps://www.blogger.com/profile/09921807758840028044noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-3526362951052079692014-07-04T08:58:51.012-04:002014-07-04T08:58:51.012-04:00168 is the order of the smallest simple group that...168 is the order of the smallest simple group that is not cyclic or alternating.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-76333514495547951712014-07-02T03:26:24.920-04:002014-07-02T03:26:24.920-04:007070 is also a number such that it and the sum of ...7070 is also a number such that it and the sum of its digits are both divisible by 14.Anonymoushttps://www.blogger.com/profile/07626605622108861596noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-74698159103712245942013-12-18T19:36:13.324-05:002013-12-18T19:36:13.324-05:00One of my favorite numbers is 648 (which is missin...One of my favorite numbers is 648 (which is missing in The Penguin Dictionary of Curious and Interesting Numbers).<br /><br />Some its properties: <br /><br />64*8 = 512 +<br />64/8 = 8 +<br />64+8 = 72 +<br />64-8 = 56 =<br />---------------------<br /> 648<br />---------------------<br /><br /><br />648 = 16² - 17² + 18² + ... + 30² - 31² + 32² = -33² + 34² - 35² + ... + 46² - 47² + 48².<br /><br />648 = 83² - 79², where 83 and 79 are consecutive primes. <br /><br />648 = 101 + 547, where 101 = prime(26) and 547 = prime(prime(26)). <br /><br />648 / (6+4+8) is a square (36).<br /><br />648 divides 53^6-1.<br /><br />Also, 648 is an Abundant number, Odious number, Smith number, Practical number, Powerful number.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-91505956053384778312013-11-24T03:12:05.082-05:002013-11-24T03:12:05.082-05:00The number 0 is also sandwiched between a perfect ...The number 0 is also sandwiched between a perfect square (1) and a perfect cube (-1)Amy W.https://www.blogger.com/profile/13567669440156307488noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-56275714264049340792013-10-04T11:10:48.505-04:002013-10-04T11:10:48.505-04:002061 is the year when Halley's Comet will retu...2061 is the year when Halley's Comet will return!Lawrence Shirleyhttp://pages.towson.edu/shirleynoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-42795837812276298752013-01-26T04:31:22.452-05:002013-01-26T04:31:22.452-05:00The last property is sated in a confusing manner (...The last property is sated in a confusing manner (the first <i>n</i> has nothing to do with the two other <i>n</i>'s in the same sentence) and it should be stated rather as follows: «<b>2225</b> has the following property: the sum<b>s</b> <i>[in the plural!]</i> of the <i>n</i>th powers of its digits <b>are</b> prime for <i>n</i> = 1 to 10 [...]»Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-64797142721094231192013-01-09T12:55:49.043-05:002013-01-09T12:55:49.043-05:00I might be being really dim, but isn't the lar...I might be being really dim, but isn't the largest number for which the absolute difference between any two digits is prime, 9742?<br />(9-7=<b>2</b>; 9-4=<b>5</b>; 9-7=<b>2</b>; 7-4=<b>3</b>; 7-2=<b>5</b>; 4-2=<b>2</b>)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-501131578777462762012-08-17T01:14:21.071-04:002012-08-17T01:14:21.071-04:00The sum of the proper factors of 70is more than 70...The sum of the proper factors of 70is more than 70, yet there is not a subset of the proper factors that adds up to 70. This is a "Weird number". 70 is the smallest weird number. Amy W.https://www.blogger.com/profile/13567669440156307488noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-76038746610412913852012-07-22T22:43:25.099-04:002012-07-22T22:43:25.099-04:00why do I see this number twice a day..for the last...why do I see this number twice a day..for the last five years? Even at the weirdest times...running through NYC, had been there for 5 hours, hadn't looked at the time in a few hours and BOOM....run into the port authority and in huge digital numbers 1029! Sometimes when I buy things, the total is 1029...now my friends see 1029....its very comforting to see this number...OH and there have been plenty of times when watching football, they stop the clock at 1029...WTFAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-1754487763246293642012-07-13T21:47:56.417-04:002012-07-13T21:47:56.417-04:00pretty insensitive the 593 boat was the USS Thresh...pretty insensitive the 593 boat was the USS Thresher - lost with all hands in 1963 - painful for family members to see this kind Hollywood oversightAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-56280063199005108052012-06-26T06:51:18.135-04:002012-06-26T06:51:18.135-04:00This is amazing!This is amazing!Daniel Oluwadamilare Akintoyehttps://www.blogger.com/profile/17278017551352678692noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-25068125072179364462012-06-11T11:59:49.749-04:002012-06-11T11:59:49.749-04:00Cool! I think my favorite number is 5...no, maybe...Cool! I think my favorite number is 5...no, maybe 2, ...or 12. No, wait, my favorite number has to be one because it allows us to get out into infinity by just adding it over and over. Yes, It's got to be one and its sidekick, simple addition... such a powerful duo! (Oops, now I'm back to 2 again!) I give up... it's like trying to pick your favorite child...impossible! (I used to be kinda partial to the square root of 2.)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-74409496196867576382012-04-17T08:18:29.666-04:002012-04-17T08:18:29.666-04:00If we extend the Pascal triangle into a Pyramid wi...If we extend the Pascal triangle into a Pyramid with square base, and assign number to the cubes like in Pascal triangle but moving inwards --like onion peels -- --eg., outermost sheath will always be numbered as 1 on all outer cubes, and so forth --- and if we do this upto 9th layer (by counting the first 1 cube at top as 1), where the numbering is 1, 8, 28, 56, 70, 56, 28, 8, 1 THEN if we add all excepting the first 1 and 1 in the second layer (as they are primordial uncreated entities), then the sum will be exactly 2183. This corresponds to the 9th layer, which in Visistadvaita begins the Brahmanda Kosa with 70 as 5th Pentatope number.<br /><br />Dr. U.A. Vinay Kumar Udupi<br />IIAS Shimla. INDIAU.A.Vinay Kumarhttps://www.blogger.com/profile/07802840967514332703noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-28999018715956355222012-04-02T21:48:09.717-04:002012-04-02T21:48:09.717-04:00I'm sorry - I can't help but comment. Wha...I'm sorry - I can't help but comment. What's special about 646? - it's the hull number of one great (former) submarine: USS GRAYLING (SSN 646) - Fast Attack Tough!! :-)Stuhttps://www.blogger.com/profile/11332999137565791777noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-46356401986179532282012-01-27T17:22:20.235-05:002012-01-27T17:22:20.235-05:00206's English name is "two hundred six&qu...206's English name is "two hundred six". Numbers only use "and" when expressing a decimal point. The first number to feature the letter A is "one thousand".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-77356454251868065512012-01-23T21:27:14.296-05:002012-01-23T21:27:14.296-05:00Is there an actual source for that "737 is th...Is there an actual source for that "737 is the smallest multidigit number m such that m^m + 2 is prime." claim? The Prime Curios! website only gives the authorJoehttp://cs.binghamton.edu/~jtannen1noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-66491446594769691722012-01-13T12:57:47.564-05:002012-01-13T12:57:47.564-05:00Algunas propiedades analíticas del número 124
Ecua...Algunas propiedades analíticas del número 124<br />Ecuación Pell: <br />4620799^2-124*414960^2=1<br />http://math.fau.edu/richman/pell-m.htm<br />Orden multiplicativo: <br />Como 12^2>124>11^2, y los primos equidistantes son 13 y 11<br />11^30=1(mód.124) es el orden multiplicativo.<br />http://www.alpertron.com.ar/DILOG.HTM<br />Formas cuadráticas sobre campos imaginarios: <br />N(a+b(-D)^(1/2)=x^2+Dy^2=124=5^2+11*3^2=7^2+3*5^2<br />124=(5+3(-11)^(1/2))(5-3(-11)^(1/2))=((7+3(-5)^(1/2))((7-3(-5)^(1/2))<br />Polinomios mínimos (PM): <br />z^2-10z+124=0, donde z=5+-3(11)^(1/)i=124<br />z^2-14z+124=0,donde z =7+-5(3)^(1/)i=124<br />Formas cuadráticas sobre campos reales: <br />N(a + b(D)^(1/2)=x^2+Dy^2=124=12^2-5*2^2=13^2-5*3^2<br />124=((12+2(5)^(1/2))((12-2(5)^(1/2))=((13+3(5)^1/2))((13-3(5)^1/2))<br />Polinomios mínimos(PM): <br />z^2-24z+124=0, donde z=2(6+-(5)^(1/2))=124<br />z^2-26z+124=0, donde z=13+-3(5)^(1/2)=124 <br />http://hojamat.es/parra/cuadrbin.pdf<br />Grupos multiplicativos: <br />Sea z=124+143t un algebraico que es un elemento de grupo multiplicativo y x=3+11t e y=7+13t los elementos aditivos de dicho grupo, donde mcd(11,13)=1=11(6)+13(-5), entonces: <br />x=3+11t=11(6)(7+13t)=33(mód.143)<br />y=7+13t=13(-6)(3+11t)=91(mód.143)<br />z=124+143t=33+91=124(mód.143), entonces <br />f(124)=f(33)+f(91) <br />http://hojamat.es/parra/iniparra.htm<br />Rafael Parra MachíoAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-80105520354537545312011-12-30T04:21:24.240-05:002011-12-30T04:21:24.240-05:00Is it not also palindromic in base 25 (1,0,1) and ...Is it not also palindromic in base 25 (1,0,1) and 312 (2,2)?Paul Coombeshttps://www.blogger.com/profile/09143484729379464693noreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-85894995366817106302011-12-24T06:10:33.625-05:002011-12-24T06:10:33.625-05:00Algunas propiedades analíticas del número 2012:
E...Algunas propiedades analíticas del número 2012: <br />Ecuación Pell: 12150478072 - 2012•270881522 = 1<br />Ver http://math.fau.edu/richman/pell-m.htm<br />Formas cuadráticas complejas: Polinomio mínimo: z^2-Sz+P= 0<br />N(a+b(-D)^(1/2) = x^2+Dy^2=41^2+331*1^2 <br />P=(41+1(-331)^(1/2)(41-1(-331)^(1/2)=2012<br />S=(41+1(-331)^(1/2)+(41-1(-331)^(1/2)=82<br />PM: z^2-82z+2012=0 => z=41+-(331)^(1/2) <br />Logaritmo discreto:<br />47^37= 43(mód.2012)<br />ver http://www.alpertron.com.ar/DILOG.HTM<br />Otras propiedades muy variadas las podrán encontrar en <br />http://hojamat.es/parra/prop2012.pdf<br />Thanks for their attention. I wish you a Merry Christmas and a Happy New Year<br />Rafael Parra MachíoAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-41175000467989791392011-12-16T05:08:28.228-05:002011-12-16T05:08:28.228-05:00Grupo multiplicativo:
Sea 23*37=851 un grupo dond...Grupo multiplicativo: <br />Sea 23*37=851 un grupo donde 743 es uno de sus elementos. <br />Si 743 se representa por el algebraico z=743+851t que es equivalente a<br />x=743(mód.23)=7 e y=743(mód.37)=3 donde<br />mcd (23,37)=1=23(-8)+37((5), entonces<br />x=23(-8)*3(mód.851)=299 e<br />y=37(5)*7(mód.851)=444, luego<br />743=23(-8)*3+37(5)*7(mód.851)=299+444 y, por tanto<br />f(743)=f(299)+f(444)<br />http://hojamat.es/parra/iniparra.htm<br />Rafael Parra MachíoAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-35575576374966493442011-12-15T13:08:35.641-05:002011-12-15T13:08:35.641-05:00Algunas propiedades analíticas del número 743
Ecua...Algunas propiedades analíticas del número 743<br />Ecuación Pell: <br />714024^2-743*26195^2=1<br />http://math.fau.edu/richman/pell-m.htm<br />Orden multiplicativo: <br />Como 28^2>743>27^2 y los primos equidistantes son 23 y 29<br />29^100=23(mód.743) es el logaritmo discreto.<br />http://www.alpertron.com.ar/DILOG.HTM<br />Formas cuadráticas sobre campos imaginarios: <br />N(a+b(-D)^(1/2)=x^2+Dy^2=743=20^2+7*7^2<br />Si el PM(polinomio mínimo) es z^2- Sz+P=0, donde<br />P=(20+7(-7)^(1/2)(20-7(-7)^(1/2)=743<br />S=(20+7(-7)^(1/2)+(20-7(-7)(1/2)= 40, entonces<br />z^2-40z+743=0, z=20+-7(-7)^(1/2)i<br />Formas cuadráticas sobre campos reales: <br />N(a+b(D)^(1/2)=x^2+Dy^2=743=29^2-2*7^2<br />Si el PM(polinomio mínimo) es z^2- Sz+P=0, donde<br />P=(29+7(2)^(1/2)(29-7(2)^(1/2)=743<br />S=(29+7(2)^(1/2)+(29-^7(2)^(1/2)=58, entonces<br />z^2-58z+743=0, z=29+-7(2)^(1/2)<br />http://hojamat.es/parra/cuadrbin.pdf<br />En general, ver:<br />http://hojamat.es/parra/iniparra.htm<br />Rafael Parra MachíoAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-30892711601025292032011-12-14T12:39:55.715-05:002011-12-14T12:39:55.715-05:00Otras propiedades del 2011 y su relación con los n...Otras propiedades del 2011 y su relación con los números primos. <br />http://hojamat.es/parra/prop2011.pdf<br />Rafael Parra Machio<br />Twitter rafaelito_pAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-72448442054444168882011-12-14T05:23:11.253-05:002011-12-14T05:23:11.253-05:00Algunas propiedades analíticas del número 647
Grup...Algunas propiedades analíticas del número 647<br />Grupos multiplicativos:<br />Como 26^2>647>25^2,667 = 23*29 donde mcd(23,29)=1=23(-5)+29(4)<br />Si z=647+667t es un número algebraico, entonces <br />x=647(mód.23)=3 e y=647(mód.29)=9, luego<br />647=23(-5)*9(mód.667)+29(4)*3 (mód.667)=299+348, por lo que <br />f(647)=f(299)+f(348) es una función multiplicativa. <br />http://hojamat.es/parra/cuadrbin.pdf <br />Grupos de primos afines:<br />647=323+323+1=2(323)+1, así x=1+2t<br />Si 23=11+12, entonces<br />647=11(q)+12(q)+3 =23(q)+3 con <br />q=28, así y=3+23t<br />Como x=1+2t e y=3+23t son equivalentes, por el Teorema Chino de Restos<br />1+2u=3(mód.23) -> 2u=2(mód.23) -> u=1(mód.23), luego<br />z=1+2(1+23t)=3+46t. <br />Este algebraico genera un grupo con características afines al 647, así<br />z = 3+46t: 3,233,463,509,601,647,739,877,1061, ... todos primos.<br />http://oeis.org/A100201<br />Rafael Parra MachíoAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1050326564532544980.post-26877926125160539292011-12-13T12:55:36.814-05:002011-12-13T12:55:36.814-05:00Algunas propiedades analíticas del número 197
Ecua...Algunas propiedades analíticas del número 197<br />Ecuación Pell: 393^2-197*28^2=1<br />http://hojamat.es/parra/cuadrbin.pdf<br />Formas cuadráticas imaginarias: <br />Si la norma es N(a+b(-D^(1/2)=x^2+D*y^2=197<br />197=7^2+37*2^2 donde z^2-14z+197=0 con z =7+-2(37)^(1/2)i<br />197=9^2+29*2^2 donde z^2-18z+197=0 con z=9+-2(29)^(1/2)i<br />197=13^2+7*2^2 donde z^2-26z+197=0 con z=13+-2(7)^(1/2)i<br />http://hojamat.es/parra/cuadrbin.pdf<br />Grupos multiplicativos<br />Como 15^2>197>14^2,210=14*15 donde mcd(14,15)=1=14(-1)+15(1)<br />Si z=197+210t es un número algebraico,entonces <br />x=197(mód.14)=1 e y=197(mód.15)=2, luego<br />197=14(-1)*2(mód.210)+15(1)*1(mód.210)=182+15,por lo que <br />f(197) = f(182)+f(15) es una función multiplicativa aditiva. <br />http://hojamat.es/parra/funesp.pdf<br />Rafael Parra MachíoAnonymousnoreply@blogger.com