Let a = 4 + f, where 0 < f < 1. We are given that (4 + f)(4 − 2f) is an integer.

This implies that 2f^{2} + 4f is an integer. Since 0 < f < 1, we have 0 < 2f^{2} + 4f < 6.

Therefore 2f^{2} + 4f can take 1, 2, 3, 4 or 5. Equating 2f^{2} + 4f to each one of them and using f > 0, we get