parmenides51 27.06.2020 23:42 Determine the integers $x$ and $y$ for which $\sqrt{4^x + 5^y}$ is rational.
electrovector 28.06.2020 00:37 Hint Write $\sqrt{4^x + 5^y}=\frac{a}{b}$ where $a, b$ relatively positive integers. Then arranging it we have $(a-b \cdot 2^x)(a+b \cdot 2^x)=5^y$. Find $gcd(a-b \cdot 2^x, a+b \cdot 2^x)$.
Darkztar 11.06.2021 17:24 Actually, all rational roots of $f(x)=0$ where $f$ is monic polynomial with integer coefficients are integers.