How many pairs (m,n) of positive integers satisfy the equation m2 + 105 = n2?
Explanation:
We know that m2 + 105 = n2
105 = n2 - m2
105 = (n + m) × (n - m)
105 can be written as 3 × 5 × 7, which can be written as product of two numbers in 4 ways i.e. (105 × 1), (35 × 3), (21 × 5), (15 × 7)
Solving each of these 4 cases will give corresponding values of m and n.
Hence, 4.
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