Question 182485
The are {{{n}}} and {{{m=n+1}}}.

We know, from the problem:

{{{2*n^2=m^2+23}}}

Subbing in the information from above,

{{{2*n^2=(n+1)^2+23}}}

Some algebra,

{{{2*n^2=n^2+2n+1+23}}}

--->

{{{n^2-2*n-24=0}}}

--->

{{{(n-6)(n+4)=0}}}

--->

{{{n=6,-4}}}

I would assume it has to be positive,  n = 6, m = 7

Checking, {{{2*6^2 = 72}}}    {{{7^2+23=72}}}

Hope this helps.