Correct Answer - Option 1 : 4

**Given:**

m^{2} + 105 = n^{2}

**Concept used:**

x^{2} - y^{2} = (x - y)(x + y)

**Calculation:**

m2 + 105 = n^{2}

m^{2} - n^{2} = 105

(m + n)(m - n) = 105

Now one needs to check the factors of 105.

105 = 1 × 3 × 5 × 7 × 15 × 21 × 35

Such possible pars are

⇒ 1 × 105

⇒ 3 × 35

⇒ 5 × 21

⇒ 7 × 15

∴ We have four such pairs of integers.