Find all triples $(x,y,z)$ of positive integers such that $$2018^x=y^2+z^2+1$$
2026-03-26 06:22:17.1774506137
Find all triples $(x,y,z)$ of positive integers such that $2018^x=y^2+z^2+1$
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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 $(44,9)$.