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

A number is increased by 20% and then decreased by 10%. What is the net change?

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

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

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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

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

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If a person can type 45 words per minute, how many words can they type in 2 hours?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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