Topic Details (Notes format)

How to Solve Simple Diophantine Equations with Two Unknowns

Subject: Mathematics

Book: Maths Mastery

A Diophantine equation restricts solutions to integers. A typical linear form is Ax + By = C. For instance, 4x + 6y= 14 can be tackled by factoring out gcd(4,6)=2, rewriting as 2(2x+3y)=14, so 2x+3y=7. Then find integer solutions systematically. Another approach is the Extended Euclidean Algorithm. These equations are fundamental in partitioning tasks, cryptographic key generation, or advanced number theory. Mastering them ensures a strong integer-based solution approach for logic puzzles or real-world quantity allocations that must remain whole.

Practice Questions

The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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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 5x - 2 = 13, what is the value of x?

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What is the sum of the first 50 positive integers?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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What is the value of x if log(x) + log(4) = log(32)?

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If the probability of an event is 1/4, what is the probability of its complement?

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What is the LCM of 15 and 20?

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If 2x - 3 = 7, what is the value of x?

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