Question: Let a, b, c be nonzero integers. prove that the diophantine equation ax+by+cz=e has an integer solution if and only if gcd(a, b, c) |

Let a, b, c be nonzero integers. prove that the diophantine equation

ax+by+cz=e has an integer solution if and only if gcd(a, b, c) | e

Hint: definition of gcd(a,b,c)

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