**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 65

^{6}- 1.

**438**is the sum of 10 positive 5th powers:

**438**= 3

^{5}+ 2

^{5}+ 2

^{5}+ 2

^{5}+ 2

^{5}+ 2

^{5}+ 2

^{5}+ 1

^{5}+ 1

^{5}+ 1

^{5}.

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:

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

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