MathDB
Problem 4

Source: 239-School Open Olympiad (Senior Level)

April 25, 2022
number theoryprimesNatural Numbers

Problem Statement

Vasya has a calculator that works with pairs of numbers. The calculator knows hoe to make a pair (x+y,x)(x+y,x) or a pair (2x+y+1,x+y+1)(2x+y+1,x+y+1) from a pair (x,y).(x,y). At the beginning, the pair (1,1)(1,1) is presented on the calculator. Prove that for any natural nn there is exactly one pair (n,k)(n,k) that can be obtained using a calculator.
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