Prove that 5^{n^3} +1 is divisible by 3^{n+1} for all nonnegative integers

pls help

i tried n=0 and found it works and now im using n=k+1 and im stuck

cphill helpp?

The statement you're trying to prove is obviously false and it's false where you said you checked. Take n = 0. Then $5^{n^3}+1 = 5^0+1 = 2$. Also, $3^{n+1} = 3^1 = 3$. Obviously 2 is not divisible by 3.