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.
If 8x = 512, what is the value of x?
View QuestionIf x:y = 2:3 and z:y = 4:3, what is x:z?
View QuestionWhat is the remainder when 5^100 is divided by 3?
View QuestionIf x + y = 10 and xy = 21, what is the value of x³ + y³?
View QuestionIf a:b = 5:7 and b:c = 6:11, what is a:c?
View QuestionIf a + b = 10 and ab = 21, what is the value of a^2 + b^2?
View QuestionIf the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?
View QuestionWhat is the square root of 121?
View QuestionIf sin(θ) = 0.6 and θ is acute, what is cos(θ)?
View QuestionA cone has a base radius of 7 cm and height of 24 cm. What is its volume?
View Question