MathDB

2014 BMT Team 19

Source:

January 6, 2022

number theory

Problem Statement

A number

k

is nice in base

b

if there exists a

k

-digit number

n

such that

n, 2n, . . . kn

are each some cyclic shifts of the digits of

n

in base

b

(for example,

2

is nice in base

5

because

2\cdot 135 = 315

). Determine all nice numbers in base

18

.

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