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2015 CHMMC Tiebreaker 1 - 2015- cube-invariant postitive integers

Source:

March 1, 2024

CHMMCnumber theorylast digitsDigits

Problem Statement

Call a positive integer

x

n

-cube-invariant if the last

n

digits of

x

are equal to the last

n

digits of

x^3

. For example,

1

n

-cube invariant for any integer

n

. How many

2015

-cube-invariant numbers

x

are there such that

x < 10^{2015}