Question

How many pairs (m, n) of positive integers
satisfy the equation m^2 + 105 = n^2 ?
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Answer 1

Answer:

Solution: Given m^2 + 105 = n^2

n^2 – m^2 = 105

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

105 can be written as 105*1 = 21*5 = 15*7 = 35*3

So, only 4 cases possible to get values of n, m as positive. Thus number of solution = 4

Answer 2

Answer:

Solution: Given m^2 + 105 = n^2

n^2 – m^2 = 105

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

105 can be written as 105*1 = 21*5 = 15*7 = 35*3

So, only 4 cases possible to get values of n, m as positive. Thus number of solution = 4