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n + T(n) = 10n, whereT(n) sends first 2 digits to the end

Source: 2021 Irish Mathematical Olympiad P3

May 30, 2021

number theoryDigitsdecimal representation

Problem Statement

For each integer

n \ge 100

we define

T(n)

to be the number obtained from

n

by moving the two leading digits to the end. For example,

T(12345) = 34512

and

T(100) = 10

. Find all integers

n \ge 100

for which

n + T(n) = 10n