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How many pairs (m,n) of positive integers satisfy the equation the equation m^2 + 105 = n^2?
How many pairs (m,n) of positive integers satisfy the equation the equation m2 + 105 = n2?
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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
Therefore 4 pair
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