Prove that $11^{2n}+5^{2n+1}-6$ is divisible with $24$ for $n∈ℤ^+$ Prove that $11^{2n}+5^{2n+1}-6$ is divisible with $24$ for $n∈ℤ^+$
I've been trying to solve it by using modulo;
$11^{2n}+5^{2n+1}-6≡ (11^2 mod24)^n + 5*(5^2mod24)^n-6 = 1^n + (5*1^n)-6 = 0$
Is this the right way to tackle the problem? I am not certain if I am placing the "$mod$" marks at the right places.

$$11^{2n}+5^{2n+1}-6=(5\cdot24+1)^n+5(24+1)^n-6\equiv 1+5-6\equiv0\pmod{24}$$
