MathDB
Sequence and divisors

Source: St Petersburg Olympiad 2011, Grade 9, P6

September 15, 2017
number theory

Problem Statement

There is infinite sequence of composite numbers a1,a2,...,a_1,a_2,..., where an+1=an−pn+anpna_{n+1}=a_n-p_n+\frac{a_n}{p_n} ; pnp_n is smallest prime divisor of ana_n. It is known, that 37∣an37|a_n for every nn. Find possible values of a1a_1
Back to ProblemsView on AoPS