Let m, n be natural numbers, and satisfy: N2 = M2 + 167, find the value of M, n

Because n ^ 2 = m ^ 2 + 167
So n ^ 2-m ^ 2 = 167, the square difference formula is: (n + m) (n-m) = 167
m. If n is a natural number, then M + N and N-M are both natural numbers, and M + n > 0, then the range of N-M is N-M > 0
And 167 = 1 × 167
So n + M = 167, N-M = 1
The sum of the two formulas is 2n = 168, n = 84
By subtracting the two formulas, 2m = 166, M = 83
So, M = 83, n = 84

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