How many primes are in the form 4n^8+1, where n is a positive integer?
*show working n explanation, PLS...
Hello
n=5p (where p is an integer) is a necessary condition but I do not know if it is a sufficient condition
If n=5p+1
Then n^8=(5p+1)^8=5P+1
Therefore 4n^8+1=20P+5 is divisible by 5 => not prime
If n=5p+2
Then n^8=(5p+2)^8=5P+2^8=5P+256
Therefore 4n^8+1=20P+1025 is divisible by 5 => not prime
If n=5p+3
Then n^8=(5p+3)^8=5P+3^8=5P+6561
Therefore 4n^8+1=20P+26245 is divisible by 5 => not prime
If n=5p+4
Then n^8=(5p+4)^8=5P+4^8=5P+65536
Therefore 4n^8+1=20P+262145 is divisible by 5 => not prime