Problem
ALG-B1-M10-P024 When the expression is prime
#24
★★★★★ Level 5 of 5
Find all integers \(n\) for which \(n^4+4\) is prime.
Use the factorization \(n^4+4=(n^2-2n+2)(n^2+2n+2)\).
We have \(n^4+4=(n^2-2n+2)(n^2+2n+2)\). For \(|n|>1\), both factors are greater than \(1\), so the number is composite. For \(n=0\), we get \(4\). For \(n=1\) and \(n=-1\), we get \(5\), which is prime. Answer: \(n=\pm1\).
The final problem of the module on a nonstandard factorization.