Friday, January 13, 2012

438

438 = 2 x 3 x 73.

438 is a Smith number because the sum of its digits is equal to the sum of the digits of its prime factors: 4 + 3 + 8 = 2 + 3 + 7 + 3 = 15.

438 is 110110110 in base 2 (binary) and 666 in base 8. It is 3223 in base 5 and 141 in base 19.

438 divides 656 - 1.

438 is the sum of 10 positive 5th powers: 438 = 35 + 25 + 25 + 25 + 25 + 25 + 25 + 15 + 15 + 15.

The term "438 match" or "438 game" has been used by cricket news media to describe the famous 2006 One Day International in which Australia scored a world record 434 in their innings, only to see South Africa respond in their innings with 438.

Source: What's Special About This Number?

1 comment:

rafparmat@gmail.com said...

Orden multiplicativo:
Como 21^2>438>20^2, y los primos equidistantes son 23 y 19
23^36(mód.438) = 1 y 19^36(mód.438) =1 son ordenes multiplicativos.
http://hojamat.es/parra/cuadrbin.pdf
Ecuación Pell
293^2-438*14^2 = 1 es la Ecuación Pell.
http://math.fau.edu/richman/pell-m.htm
http://hojamat.es/parra/cuadrbin.pdf
438=3[(1+i)(1-i)(8+3i)(8-3i)] factorización conjugada.
438=3[(1+i)(1+i)(-i)(8+3i)(3+8i)(-i)] factorización asociada a la unidad.
http://en.wikipedia.org/wiki/Gaussian_integer
http://hojamat.es/parra/gaussiana.pdf
438=x^2+Dy^2 = 17^2+149*1^2
438=(17+(-149)^(1/2)) (17-(-149)^(1/2)=17+-(149)^(1/2))i.
438=x^2+Dy^2 = 31^2-523*1^2
438=(31+(523)^(1/2)) (31-(523)^(1/2))=31+-(523)^(1/2))
http://hojamat.es/parra/cuadrbin.pdf
Sea m=a*b=17*9=493,con mcd(17,29)=1=17(12)+19(-7),
donde z=438+493t y x=13+17t e y=3+29t
x=13+17t=17(12)(3+29t)=119(mód.493)
y=3+29t=29(-7)(13+17t)=319 (mód.493)
z=438+493t=119+319=438(mód.493) de donde
f(438)=f(119)+f(319)
438(mód.17)=13=4x^2+9y=13(mód.17)
x=6+17t=4(6+17t)^2=8(mód.17)
y=10+17t=9(10+17t)=5(mód.17)
z=8+5=13(mód.17)
http://hojamat.es/parra/iniparra.htm
Rafael Parra Machío