2n-m is a multiple of 3. It is proved that the square of 8N + the square of 10mn-7m is a multiple of 9, where Mn is an integer

Let 2n-m = 3K and K be an integer
Then: M = 2n-3k
So: 8N ^ 2 + 10mn-7m ^ 2
=8n^2+10(2n-3k)n-7(2n-3k)^2
=54kn-9k^2
=9*(6kn-k^2)
Where K and N are integers
So: 8N ^ 2 + 10mn-7m ^ 2 is a multiple of 9

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