<s>[INST] Is $\frac{a^2+b^2}{2}=c^2$ possible? I am looking for an integer solution to the equation:
$$\frac{a^2+b^2}{2}=c^2(a\neq b\neq c)$$
That is a square number that is the mean of two other square numbers, is this possible? And if so please can you give me an example?
 [/INST] We know that $(x-y)^2+(x+y)^2=2(x^2+y^2).$
So, if $a=x+y$ and $b=x-y$, then $c^2=x^2+y^2.$ 
Now see Formulas for generating Pythagorean triples.
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