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Question 22 : How many pairs (m,n) of positive integers satisfy the equation the equation m2 + 105 = n2? [TITA]

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Explanatory Answer

We know that m2 + 105 = n2
105 = n2 - m2
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 m2 + 105 = n2? [TITA] "

Hence, the answer is 4


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