Question

How many pairs of (m, n) of positive integers satisfy the equation m² + 105 = n² ?
1. 4
2. 2
3. 1
4. 3

Answer 1

Correct Answer - Option 1 : 4

Given:

m² + 105 = n²

Concept used:

x² - y² = (x - y)(x + y)

Calculation:

m2 + 105 = n²

m² - n² = 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.