MathDB
2020 PUMaC NT A8

Source:

January 1, 2022
number theory

Problem Statement

What is the smallest integer a0a_0 such that, for every positive integer nn, there exists a sequence of positive integers a0,a1,...,an−1,ana_0, a_1, ..., a_{n-1}, a_n such that the first n−1n-1 are all distinct, a0=ana_0 = a_n, and for 0≤i≤n−10 \le i \le n -1, aiai+1a_i^{a_{i+1}} ends in the digits 0ai‾\overline{0a_i} when expressed without leading zeros in base 1010.
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