**124**= 2

^{2}x 31.

**124**is 444 in base 5.

**124**is the smallest number whose sum of digits (1 + 2 + 4 = 7) as well as the number itself are one less than the cube of a prime.

**124**is the smallest number with the property that its first three multiples contain the digit 2: 124, 248, and 372.

**124**is the sum of eight consecutive primes:

**124**= 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.

**124**= 2

^{7}- 2

^{2}.

**124**= 5

^{2}+ 5

^{2}+ 5

^{2}+ 7

^{2}.

**124**was a family car produced in Italy from 1966 to 1974.

Source: Prime Curios!

## 1 comment:

Algunas propiedades analíticas del número 124

Ecuación Pell:

4620799^2-124*414960^2=1

http://math.fau.edu/richman/pell-m.htm

Orden multiplicativo:

Como 12^2>124>11^2, y los primos equidistantes son 13 y 11

11^30=1(mód.124) es el orden multiplicativo.

http://www.alpertron.com.ar/DILOG.HTM

Formas cuadráticas sobre campos imaginarios:

N(a+b(-D)^(1/2)=x^2+Dy^2=124=5^2+11*3^2=7^2+3*5^2

124=(5+3(-11)^(1/2))(5-3(-11)^(1/2))=((7+3(-5)^(1/2))((7-3(-5)^(1/2))

Polinomios mínimos (PM):

z^2-10z+124=0, donde z=5+-3(11)^(1/)i=124

z^2-14z+124=0,donde z =7+-5(3)^(1/)i=124

Formas cuadráticas sobre campos reales:

N(a + b(D)^(1/2)=x^2+Dy^2=124=12^2-5*2^2=13^2-5*3^2

124=((12+2(5)^(1/2))((12-2(5)^(1/2))=((13+3(5)^1/2))((13-3(5)^1/2))

Polinomios mínimos(PM):

z^2-24z+124=0, donde z=2(6+-(5)^(1/2))=124

z^2-26z+124=0, donde z=13+-3(5)^(1/2)=124

http://hojamat.es/parra/cuadrbin.pdf

Grupos multiplicativos:

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:

x=3+11t=11(6)(7+13t)=33(mód.143)

y=7+13t=13(-6)(3+11t)=91(mód.143)

z=124+143t=33+91=124(mód.143), entonces

f(124)=f(33)+f(91)

http://hojamat.es/parra/iniparra.htm

Rafael Parra Machío

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