How many pairs of positive integers(of m,n) satisfy the equation m² + 105 = n²

How many pairs of positive integers(of m,n) satisfy the equation m² + 105 = n²

a)            2

b)            3

c)            4

d)            5

Sol:

m² – n² = 105

(m – n) (n + m) = 105

105 = 3 × 35 ⇒ m = 19, n = 16

105 = 5 × 21 ⇒ m = 13, n = 8

105 = 7 × 15 ⇒ m = 11, n = 4

⇒ 3 pairs of (m, n)