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

If x^2 - 5x + 6 = 0, what are the roots?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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

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What is the area of a circle with a diameter of 14 cm?

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

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If the sum of three consecutive integers is 72, what are the integers?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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A sphere has a radius of 7 cm. What is its volume?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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