# From SAMC

• Let $F_0 = 0, F_1 = 1$ and $F_{{n+1}} = F_{n} + F_{n-1}$, for all positive integers $n$, be
the Fibonacci sequence. Prove that for any positive integer $m$ there exist
infi nitely many positive integers $n$ such that :
$F_n+2\equiv F_{n+1}+1 \equiv F_{n+2} \,\, [m].$

Looks like your connection to Expii Forum was lost, please wait while we try to reconnect.