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max interchangeable 4-digit May Olympiad (Olimpiada de Mayo) 2016 L2 P1

Source:

September 25, 2021

number theoryDigits

Problem Statement

We say that a four-digit number

\overline{abcd}

, which starts at

a

and ends at

d

, is interchangeable if there is an integer

n >1

such that

n \times \overline{abcd}

is a four-digit number that begins with

d

and ends with

a

. For example,

1009

is interchangeable since

1009\times 9=9081

. Find the largest interchangeable number.

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