2.) By Theorem 3.23 of the text, the linear diophantine equation of the form ax +...

2.) By Theorem 3.23 of the text, the linear diophantine equation of the form ax + by = c has no integral solutions if c is not divisible by (a, b), the greatest common divisor of a and b. On the other hand if (a, b) divides c, then we can use the Extended Euclidean Algorithm to find integers s, t such that sa + tb = (a, b); multiplying through by the correct factor gives an integral solution x, y. Write a Mathematica procedure that solves any linear diophantine equation of the form ax + by = c, whenever it is solvable. You should invoke your Extended Euclidean Algorithm.

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Colby Messinger answered 2 years ago

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please tell me how to write proofs for diophantine equation

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