Tribonacci numbers and primes of the form $p=x^2+11y^2$

Tim Evink, Paul Alexander Helminck

In this paper we show that for any prime number $p$ not equal to $11$ or $19$, the Tribonacci number $T_{p-1}$ is divisible by $p$ if and only if $p$ is of the form $x^2+11y^2$. We…