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Question 22 : How many pairs (m,n) of positive integers satisfy the equation the equation m^{2} + 105 = n^{2}? [TITA]

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We know that m^{2} + 105 = n^{2}

105 = n^{2 }- m^{2}

105 = (n+m) (n-m)

105 can be written as 3 x 5 x 7, which can be written in 4 ways

(1 x 105), (3 x 35), (5 x 21), (7 x 15) can be the possible values of m and n respectively

4 pairs

The question is **"How many pairs (m,n) of positive integers satisfy the equation the equation m ^{2} + 105 = n^{2}? [TITA] " **

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