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

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

View Question

If x:y = 4:5 and y:z = 2:3, what is x:z?

View Question

What is the cube root of 729?

View Question

If the average of five consecutive odd numbers is 25, what is the largest number?

View Question

A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

View Question

What is the HCF of 72 and 120?

View Question

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

View Question

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

View Question

If the sum of three consecutive integers is 72, what are the integers?

View Question

A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

View Question