MathDB

6

Part of 2004 India Regional Mathematical Olympiad

Problems(1)

Primes

Source: Indian RMO 2004 Problem 6

2/28/2006
Let p1,p2,…p_1, p_2, \ldots be a sequence of primes such that p1=2p_1 =2 and for n≥1,pn+1n\geq 1, p_{n+1} is the largest prime factor of p1p2…pn+1p_1 p_2 \ldots p_n +1 . Prove that pn≠5p_n \not= 5 for any nn.
modular arithmeticnumber theoryrelatively prime