tag:blogger.com,1999:blog-1050326564532544980.post1588172252479692626..comments2024-03-22T20:09:53.724-04:00Comments on NumberADay: 677Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-1050326564532544980.post-84836086687295759022010-07-23T14:02:15.459-04:002010-07-23T14:02:15.459-04:00Other properties of the number 677
677 can be repr...Other properties of the number 677<br />677 can be represented as 677=3^6-52<br />677 divides 26^4-1<br />677 can be represented as other Pythagorean triples: 677^2=70200^2 +452921^2 or 677^2+229124^2=229125 ^2<br />677 Fermat's cousin and that 677=2k+1=2*338 and 677=4k+1=4*169. It is a number that, as mentioned, can be represented as the sum of two squares, then, is a Gaussian integer, then<br />677=(26+i)(26-i) as a reciprocal or conjugate or<br />677=(26+i)(1+26i)(-i) as in factorization with symmetric unit<br />Using the conjecture of Albert Girard that every number can be a square sum of plus or minus another number multiplied by a square of 2 or more a square-minus the sum of prime, we can establish that, 677 has the representation:<br />677=4^2+661=6^2+677=8^2+613=10^2+577<br />677=3^2+167*2^2=5^2+163*2^2=7^2+153*2^2=9^2+149*2^2<br />or<br />677=28^2-107=30^2-223=32^2-347=34^2-479 =36^2-619<br />677=27^2-13*2^2=29^2-41*2^2 =31^2-71*2^2=33^2-103*2^2=35^2-137*2^2<br />677 is a typical number that allows a teacher to develop a masterclass on the unique factorization in quadratic fields.<br />A curiosity: The Angelo's 677 Prime in Albany a restaurant, view<br />http://www.677prime_wedding_events<br />Rafael Parra DE BarcelonaAnonymousnoreply@blogger.com