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

What is the sum of the first 50 positive integers?

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The area of an equilateral triangle with side length 6 cm is:

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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What is the sum of the first 20 odd numbers?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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If x^2 + 4x + 4 = 0, what is the value of x?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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