Hi this is a hard thing. Solving Diophantine equations with many variables. My mind hang with this. Somebody helps me. This is it:
x+y congruence to 1(mod7)
x+z congruence to 2(mod7)
y+z congruence to 3(mod7)
Hi this is a hard thing. Solving Diophantine equations with many variables. My mind hang with this. Somebody helps me. This is it:
x+y congruence to 1(mod7)
x+z congruence to 2(mod7)
y+z congruence to 3(mod7)
Write x + y = 1 + 7k , x + z = 2 + 7m , y + z = 3 + 7n , k,m,n integers.
Substract now the 3rd. one from the 1st.:
x - z = -2 + 7(k-n) , and now add this to the second one
2x = 7(k-n+m) ==> x = 0 (mod 7), and from here y = 1 (mod 7), z = 2(mod 7), and the general solution is:
x = 7k
y = 1 + 7m
z = 2 + 7n
k,m,n integers.
Tonio