%%visits: 2 Diophantine equations :~ Polynomial equations with integer coefficients, we seek integer solutions, ax + by = c ## intuition Let a, b, c be integers, with a and b not both 0, and let d = gcd(a, b). The equation ax + by=… :todo: Now finding all solutions has a link to a line, specifically the rise over run, is the adding of x and take away of y :todo: ## rigour ## exam clinic Fnd all integer solutions (or explain why there are no integer solutions) to the equation 52x + 93y = 7 - Steps, find gcd(52,93) - If gcd|7 - Use the [[Bezouts_lemma]] and multiply the equation by 7. ## resources tags :math:introduction_to_abstract_algebra:introduction_to_number_theory: