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

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

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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

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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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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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