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

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What is the value of log₃(27)?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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

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If the radius of a circle is 7 cm, what is its circumference?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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What is the LCM of 15 and 20?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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