MathDB

Problem 1

Part of 1980 Bulgaria National Olympiad

Problems(1)

decimal digits, unique sequence existence

Source: Bulgaria 1980 P1

6/17/2021
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.
algebraDigitsnumber theory