JEE Advanced Maths: Theory of Equations / Number Theory questions with solutions

Q1. Find all integral solutions (x, y) of the equation x*y - y - 2*x = 3.

1. (6, 3)
2. (2, 7)
3. (0, -3)
4. (-4, 1)

Answer: (6, 3)

Factoring gives (x - 1)(y - 2) = 5. The integer factor pairs of 5 give all integral (x, y). Checking the options against these pairs identifies the valid one.