$2^{4n}+1$ cannot be a prime if $3|n$ and $n>0$
My Try:
$$2^{12k}+1\equiv (-1)^{3k}+1 \equiv0\pmod{17}$$
So it divisible by $17$ for odd $k$. But how to complete the proof?
Answer
Hint: $$ 16^{3k} +1 = (16^k+1)(16^{2k}-16^k+1).$$
$2^{4n}+1$ cannot be a prime if $3|n$ and $n>0$
My Try:
$$2^{12k}+1\equiv (-1)^{3k}+1 \equiv0\pmod{17}$$
So it divisible by $17$ for odd $k$. But how to complete the proof?
Answer
Hint: $$ 16^{3k} +1 = (16^k+1)(16^{2k}-16^k+1).$$
No comments:
Post a Comment