MathDB

Unique set of residues

Source: Kvant Magazine No. 10 2022 M2719

March 8, 2023

Kvantnumber theoryresidue

Problem Statement

For an odd positive integer

n>1

define

S_n

to be the set of the residues of the powers of two, modulo

n{}

. Do there exist distinct

n{}

and

m{}

whose corresponding sets

S_n

and

S_m

coincide?
Proposed by D. Kuznetsov