MathDB
S_n + 1 is divisible by 2^{n-2} (VI Soros Olympiad 1990-00 R1 8.8)

Source:

May 27, 2024
number theory

Problem Statement

Let p1p_1, p2p_2, ......, pnp_n be different prime numbers (n≥2n\ge 2). All possible products containing an even number of coefficients (all coefficients are different) are composed of these numbers. Let SnS_n be the sum of all such products. For example, S4=p1p2+p1p3+p1p4+p2p3+p2p4+p3p4+p1p2p3p4.S_4 = p_1p_2 + p_1p_3 + p_1p_4 + p_2p_3 + p_2p_4 + p_3p_4+ p_1p_2p_3p_4. Prove that Sn+1S_n + 1 is divisible by 2n−22^{n-2}.
Back to ProblemsView on AoPS