Question 1114873
Integers n-1, n, n+1

{{{(n+1)^2=(n-1)^2+n^2-320}}}

-

{{{n^2+2n+1=n^2-2n+1+n^2-320}}}
{{{2n+1=-2n+1+n^2-320}}}
{{{0=-4n+n^2-320}}}
{{{n^2-4n-320=0}}}

{{{n=(4+- 36)/2}}}

{{{system(n=20, or, n=-16)}}}


One or both of these should work:
-17, -16, -15
OR
19, 20, 21.