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InterviewSolution
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How many pairs (m, n) of positive integers satisfy the equation m2 + 105 = n2? (type in box) |
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Answer» Calculation: m2 + 105 = n2 ⇒ n2 – m2 = 105 ⇒ (n – m)(n + m) = 105 n, m are positive integer Factor of 105 = 1, 3, 5, 7, 15, 21, 35, 105 ⇒ n + m > n – m Condition, n + m = 105 & n – m = 1 Solve m & n ⇒ n = 53, m = 52 n + m = 35 & n – m = 3 Solve m & n ⇒ n = 19, m = 16 n + m = 21 & n – m = 5 Solve m & n ⇒ n = 13, m = 8 n + m = 15 & n – m = 7 Solve m & n ⇒ n = 11, m = 4 ∴ There are four pair. |
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