MathDB

Let

a,b,c

be real numbers such that

ab\not= 0

and

c>0

. Let

(a_{n})_{n\geq 1}

be the sequence of real numbers defined by:

a_{1}=a, a_{2}=b

and

a_{n+1}=\frac{a_{n}^{2}+c}{a_{n-1}}

for all

n\geq 2

. Show that all the terms of the sequence are integer numbers if and only if the numbers

a,b

and

\frac{a^{2}+b^{2}+c}{ab}

are integers.

Problem Statement