Question 5
a) Find all integers $m \geqslant 1$ and $n \geqslant 1$ such that $\frac{5^{m}+2^{n+1}}{5^{m}-2^{n+1}}$ is the square of an integer.
b) More generally, find all integers $m \geqslant 1$ and $n \geqslant 1$, together with the primes $p$, such that $\frac{5^{m}+2^{n} p}{5^{m}-2^{n} p}$ is the square of an integer.
b) More generally, find all integers $m \geqslant 1$ and $n \geqslant 1$, together with the primes $p$, such that $\frac{5^{m}+2^{n} p}{5^{m}-2^{n} p}$ is the square of an integer.