so we have that a=2 is a misleader and the question is 1. let p>5 be prime and let n= 4^(p)+1/5 show that n is an integer
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$\displaystyle 4^p+1$ is divisible by $\displaystyle 5$ for any odd positive integer $\displaystyle p,$ not just odd primes. Hint: $\displaystyle 4^p+1=(5-1)^p+1.$
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