Competition problem — Number theory

Library / /12 of 50

Number theory Difficulty 5.1 AIME, harder Prove it Belarus

Find all pairs $(m, n)$ of nonnegative integers for which
$m^2 + 2 \cdot 3^n = m(2^{n+1} - 1).$

Solution

2. See IMO-2010 Shortlist, Problem N2.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.