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decimal digits, unique sequence existence

Source: Bulgaria 1980 P1

June 17, 2021
algebraDigitsnumber theory

Problem Statement

Show that there exists a unique sequence of decimal digits p0=5,p1,p2,…p_0=5,p_1,p_2,\ldots such that, for any kk, the square of any positive integer ending with pkpk−1⋯p0‾\overline{p_kp_{k-1}\cdots p_0} ends with the same digits.
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