2014 · Q1
What is the number of integral solutions of the equations HCF (a, b) = 5 and a + b = 65?
Elementary MathematicsNumber System
- ANone
- BInfinitely many
- CLess than 65
- DExactly one
Explanation
Writing a = 5x, b = 5y with coprime x, y gives x + y = 13, which has infinitely many coprime pairs; e.g. x = 1..12 with gcd(x, 13-x) = 1 gives infinitely many solutions.