Question 6
Let $a$ and $b$ be positive integers such that
$\varphi(ab+1)$ divides $a^2+b^2+1$.
Prove that $a$ and $b$ are Fibonacci numbers.
Proposed by Raymond Feng and Eric Shen.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.
$\varphi(ab+1)$ divides $a^2+b^2+1$.
Prove that $a$ and $b$ are Fibonacci numbers.
Proposed by Raymond Feng and Eric Shen.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.