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.
If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?
View QuestionIf two complementary angles differ by 30°, what are the angles?
View QuestionWhat is the remainder when 5^100 is divided by 3?
View QuestionIf log(100) = 2 and log(10) = 1, what is log(1000)?
View QuestionIf a:b = 2:3 and b:c = 4:5, what is a:c?
View QuestionIf a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?
View QuestionIf a+b = 10 and ab = 21, what is the value of (a-b)^2?
View QuestionThe sum of the squares of two consecutive integers is 145. What are the integers?
View QuestionIf sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?
View QuestionA square is inscribed in a circle with a radius of 5 cm. What is the area of the square?
View Question