MathDB

4

Part of 2023 Czech and Slovak Olympiad III A.

Problems(1)

SKMO 2023 P4

Source: czechoslovak national mo round

4/4/2023
Let (an)n=0∞(a_n)_{n = 0}^{\infty} be a sequence of positive integers such that for every n≥0n \geq 0 it is true that an+2=a0a1+a1a2+...+anan+1−1a_{n+2} = a_0 a_1 + a_1 a_2 + ... + a_n a_{n+1} - 1 a) Prove that there exist a prime number which divides infinitely many ana_n b) Prove that there exist infinitely many such prime numbers
number theoryprime numbers