MathDB

k+σ(k)=2^n, permutation of [20]

Source: VTRMC 2005 P2

June 10, 2021

number theory

Problem Statement

Find, and write out explicitly, a permutation

\{p(1),p(2),\ldots,p(20)\}

\{1,2,\ldots,20\}

such that

k+p(k)

is a power of

2

for

k=1,2,\ldots,20

, and prove that only one such permutation exists.