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first digit is moved to the end of the number, it increases by 60 %

Source: Singapore Open Math Olympiad 2000 2nd Round p3 SMO

April 2, 2020
number theoryDigits

Problem Statement

Is there a positive integer with at most four digits whose value is increased by exactly 60%60\% when the first digit is moved to the end of the number? For example, when the first digit of 12341234 is moved to the end of the number, the result is the integer 23412341.
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