Problem 3 Let a. b and c be positive integers satisfving the equation

(a.b) + [a.b] = 2021^c.

If |a-b| is a prime number, prove that the number (a + b)² + 4 is composite.

Here, (a.b) denotes the greatest common divisor of a and b. and [a. b] denotes the least common multipie of a and b.