MathDB
(a_1 - 1)(a_2 - 1)(a_3 -1)...(a_k - 1) divides a_1a_2a_3 ...a_k + 1

Source: Indian Postal Coaching 2008 set 1 p3

May 25, 2020
number theoryProductdividesdivisible

Problem Statement

Prove that there exists an in nite sequence <an><a_n> of positive integers such that for each k≥1k \ge 1
(a1−1)(a2−1)(a3−1)...(ak−1)(a_1 - 1)(a_2 - 1)(a_3 -1)...(a_k - 1) divides a1a2a3...ak+1a_1a_2a_3 ...a_k + 1.
Back to ProblemsView on AoPS