Thread: congruence modulo

if x^3+4y^3 + 7z^3 is congruent to 0 mod 9 and gcd(x,y,z)=1, why does it mean that x=y=z=o?

Originally Posted by alexandrabel90

if x^3+4y^3 + 7z^3 is congruent to 0 mod 9 and gcd(x,y,z)=1, why does it mean that x=y=z=o?

Hint: Compute the possible values of x³, y³ and z³ mod 9. Then compute the possible values of 4y³ and 7z³ mod 9.

Please post again if this hint isn't clear, or if you need more hints.

i found that x^3, y^3 and z^3 have to be congruent to 0 mod 9...hence i can conclude that they are all zero?

Originally Posted by alexandrabel90

i found that x^3, y^3 and z^3 have to be congruent to 0 mod 9...hence i can conclude that they are all zero?

Hint: Use the fact that gcd(x,y,z) = 1.

Originally Posted by alexandrabel90

i found that x^3, y^3 and z^3 have to be congruent to 0 mod 9...hence i can conclude that they are all zero?

Just because their greatest commond divisor is 1 doesn't make them all equal zero. They could be all relativaly prime to each other.