Question

Find the number of positive integers n for which m + 96 is a perfect square. please explain it for a dummy like me of class 6 (I know factorizing)​

Answer 1

Answer:

Suppose that n2 + 96 = m2 for some positive integer m, then

m2 - n2 = 96

(m - n)(m + n) = 96 = 25 × 3

96 has 12 divisors which come in pairs and since m - n < m + n they are

m - n m + n

1 96

2 48

3 32

4 24

6 16

8 12

For each of the 6 cases solve for m and n and verify which pairs, if any, satisfy your requirements.

Step-by-step explanation:

Hope it helps you......