1. ## 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?

2. ## Re: congruence modulo

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.

3. ## Re: congruence modulo

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?

4. ## Re: congruence modulo

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.

5. ## Re: congruence modulo

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.