Topic Details (Notes format)

How to Solve Linear Diophantine Equations (Ax + By = C)

Subject: Mathematics

Book: Maths Mastery

A linear Diophantine equation in two variables, Ax + By = C, seeks integer solutions. Using the Extended Euclidean Algorithm helps find one solution (x₀, y₀), and the full solution set stems from x=x₀+(B/d)n, y=y₀–(A/d)n, where d=gcd(A,B). For example, 6x + 9y = 3 has infinite integer solutions once you find one. Diophantine equations appear in integer partitioning tasks, cryptography (modular arithmetic), and number theory. Mastering them fosters advanced problem-solving skills across discrete math and computational contexts.

Practice Questions

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A number is increased by 20% and then decreased by 20%. What is the net change?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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