# [proposed] NT EXO

• Prove that the equation in $(a,b,c,n)$ $a^2 + b^2 + c^2 = 2^nabc$ has no positive integer solutions.

• WLOG $c$ is even , then mod 4 we deduce that $a^2+b^2 \equiv 0$ hence the three are even
Now we write $a=2a_1$ and similarly for $b_1$ and $c_1$, we repeat the same argument to get an infinite descent in positive integers, which is impossible ..

• @Abdellah-Elmrini
yes it's just the infinite descent

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