MathDB

6

Part of 2018 Vietnam National Olympiad

Problems(1)

VMO 2018 P6

Source: Vietnam MO 2nd day 2nd problem

1/12/2018
The sequence (xn)(x_n) is defined as follows: x0=2, x1=1, xn+2=xn+1+xnx_0=2,\, x_1=1,\, x_{n+2}=x_{n+1}+x_n for every non-negative integer nn. a. For each n≥1n\geq 1, prove that xnx_n is a prime number only if nn is a prime number or nn has no odd prime divisors b. Find all non-negative pairs of integers (m,n)(m,n) such that xm∣xnx_m|x_n.
Sequencenumber theory