Question

The largest known prime number is
\[\huge 2^{43112609} − 1\]
the largest integer that is currently known to be a prime number.

how many positive integers n are there for which
\[\huge n^4+n^2+1\]
is a prime

Answer 1

=> n^4 + 2n^2 -n^2 +1 = (n^2 +1)^2 -n^2 = (n^2 +n+1)(n^2 -n +1)
since it is a factor of 2 terms, it wont be prime
unless
n^2 -n +1 = 1 or n^2 +n + 1 =1
=>n=0,1 and -1
since its asking for n>0, i'd say n=1 is the only ans..

Answer 2

nice work @shubhamsrg

Answer 3

hmm.. :)