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Part of Bangladesh Mathematical Olympiad 2020 Final

Problems(1)

Bangladesh Mathematical Olympiad 2020 Final

Source: BdMO Final 2020 Primary Category Problem 1

8/30/2020
A pair of positive integers (m,n)(m,n) is called 'steakmaker' if they maintain the equation 1 + 2m^m = n2^2. For which values of m and n, the pair (m,n)(m,n) are steakmaker, find the sum of mnmn
number theory