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

If a number is divisible by 9, it is also divisible by which of the following?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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The probability of getting an even number when rolling a die is:

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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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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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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

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

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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If 8x = 512, what is the value of x?

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