Question

The number of natural number n for which n² + 96 is a perfect square is _____.

Answer 1

n² + 96 = k²

k² – n² = 96

(k – n) (k + n) = 96 × 1

= 48 × 2

= 24 × 4

= 12 × 8

= 16 × 6

= 32 × 3

n = 23, 10, 2, 5

so number of values of n is 4.