Oldie but a goodie...
- --- In email@example.com,
Jack Brennen <jfb@...> wrote:
> Find all primes of the form 4^n+n^4,Let f(n) = 4^n + n^4.
> where n is a positive integer.
If n is even, then so is f(n).
If n is odd, then
f(n) = (A(n) + B(n))*(A(n) - B(n))
A(n) = 2^n + n^2
B(n) = 2^((n+1)/2)*n
Hence only f(1) = 5 is prime.
Not also that 5|f(n) if n is odd and coprime to 5.
David (per proxy Léon François Antoine)
- --- On Wed, 7/1/09, Jack Brennen <jfb@...> wrote:
> Quick little prime chestnut for you:Ah - memories of http://www.leyland.vispa.com/numth/primes/xyyx.htm
> Find all primes of the form 4^n+n^4, where n is a positive integer.