MathDB

6

Part of 1984 Poland - Second Round

Problems(1)

x_1=c,\; x_{n+1} = cx_n + \sqrt{(c^2-1)(x_n^2-1)}

Source: Polish MO Recond Round 1984 p6

9/9/2024
The sequence (xn)(x_n) is defined by formulas x_1=c,\; x_{n+1} = cx_n + \sqrt{(c^2-1)(x_n^2-1)}  \text{ for }  n=1,2,\ldots Prove that if c c is a natural number, then all numbers xn x_n are natural.
number theorySequencerecurrence relation