IMO 2007 Shortlist N4

For every integer k ≥ 2, prove that 23k divides the number  2k+1 2k  −  2k 2k−1  (1) but 23k+1 does not. (Poland)

imomathematicsolympiadshortlistnumber-theory

IMO 2007 Shortlist N4

Category: Number Theory

Problem

For every integer k ≥ 2, prove that 23k divides the number  2k+1 2k  −  2k 2k−1  (1) but 23k+1 does not. (Poland)