\(\displaystyle \sqrt{x}=t\).

The last digit of \(\displaystyle 169^{t} +144^{t}-2\cdot 156^{t}\) must be \(\displaystyle 5\).

The last digit of \(\displaystyle 169^{t} +144^{t}\) or \(\displaystyle 9^{t}+4^{t} \) must be \(\displaystyle 7\) , which happens for \(\displaystyle t=2\) or \(\displaystyle x=4\).

https://brilliant.org/wiki/finding-the-last-digit-of-a-power/

The last digit of \(\displaystyle 169^{t} +144^{t}-2\cdot 156^{t}\) must be \(\displaystyle 5\).

The last digit of \(\displaystyle 169^{t} +144^{t}\) or \(\displaystyle 9^{t}+4^{t} \) must be \(\displaystyle 7\) , which happens for \(\displaystyle t=2\) or \(\displaystyle x=4\).

https://brilliant.org/wiki/finding-the-last-digit-of-a-power/

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