124 = 22 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 = 27 - 22.
124 = 52 + 52 + 52 + 72.
The Fiat 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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