# Find all triples $(x,y,z)$ of positive integers such that $2018^x=y^2+z^2+1$ [closed]

Find all triples $(x,y,z)$ of positive integers such that $$2018^x=y^2+z^2+1$$

## closed as off-topic by GNUSupporter 8964民主女神 地下教會, Did, Namaste, user223391, erfinkApr 28 '18 at 19:19

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• Immediately $x$ must be odd – lab bhattacharjee Apr 27 '18 at 9:44
• Why $2018{}{}$? – Lord Shark the Unknown Apr 27 '18 at 9:45
• Seems like some math contest stuff... – Thern Apr 27 '18 at 9:47
• HINT: Look at this equation modulo $4$. You can easily see that necessarily $x<2$. Then the equation becomes $$z^2+y^2=2017$$ which has only two symmetric solutions $(9,44)$ or $(44,9)$. – Crostul Apr 27 '18 at 9:53

HINT: Look at this equation modulo $4$. You can easily see that necessarily $x<2$ (i.e. $x=1$).
Then the equation becomes $$z^2+y^2=2017$$ which has only two symmetric solutions $(9,44)$ or $(44,9)$.