2021/051) Prove that $\frac{5^{125}-1}{5^{25}-1}$ is a composite number

Let $f(x) = x^4 + x^3 + x^2 + x+ 1$
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we get $f(x) = (x^2 + 1)^2 + x^3 - x^2 + x$

$= (x^3 + 3x + 1)^2 - 2* 3x(x^2+1) - 9x^2 + x^3 - x^2 + x$

$= (x^2 + 3x + 1) ^2 - (5x^3 + 10x^2 + 5x)$

$= (x^2 + 3x +1^2 - 5x(x+1)^2$

$\frac{5^{125}-1}{5^{25}-1} = f(5^{25})$

$f(5^{25}) =  (5^{50} + 3 * 5^{25} +1)^2 - 5 * 5^{25}(5^{25}+1)^2$

$= (5^{50} + 3 * 5^{25} +1)^2 - (5^{13}(5^{25}+1))^2$

$= (5^{50} + 3 * 5^{25} +1 + (5^{13}(5^{25}+1))(5^{50} + 3 * 5^{25} +1 - (5^{13}(5^{25}+1))$

product of 2 numbers neither is 1 so composite