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?
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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 x^{3}, y^{3} and z^{3} mod 9. Then compute the possible values of 4y^{3} and 7z^{3} 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.
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