Write two positive integers m, n (m)

Write two positive integers m, n (m)

∵115=23×5
And there are: 3 & # 178; + 4 & # 178; = 5 & # 178;
∴(3×23)²+(4×23)²=(5×23)²
∴,M=3×23=69
N=4×23=92

If M and N are positive integers and the square of M + 2n = the square of N + 2m + 5, what is the value of N?

(m-1) ^ 2 = (n-1) ^ 2 + 5, so, (m-1) ^ 2 = 9, (n-1) ^ 2 = 4, M = 4, n = 3

(a-b) ^ m * (a-b) ^ n * (B-A) ^ 2n * (B-A) ^ 2m + 1 (M / N is a positive integer)

Because m is a positive integer
Then 2n is even and 2m + 1 is odd
(a-b)^m*(a-b)^n*(b-a)^2n*(b-a)^2m+1
=(a-b)^m*(a-b)^n*(a-b)^2n*(a-b)^(2m+1)*(-1)
=-(a-b)^(m+n+2n+2m+1)
=-(a-b)^(3m+3n+1)