How many pairs of positive integers(of m,n) satisfy the equation m² + 105 = n²
a) 2
b) 3
c) 4
d) 5
Sol:
m² – n² = 105
(m – n) (n + m) = 105
105 = 3 × 35 ⇒ m = 19, n = 16
105 = 5 × 21 ⇒ m = 13, n = 8
105 = 7 × 15 ⇒ m = 11, n = 4
⇒ 3 pairs of (m, n)
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