2000 character limit reached
Chutes and Ladders: on some sequences inspired by 2017 Putnam A1
Published 25 May 2024 in math.CO and math.NT | (2405.16068v1)
Abstract: The first problem of the 2017 Putnam competition was to characterize a set of natural numbers closed under both the square-root map and the "add 5 and square" map . We reframe this as a problem on an infinite directed graph, using this framing both to generalize the problem and its solution, as well as to determine the first appearance of each number in this set under a row-wise algorithm that outputs all its elements.
- Guy Chassé. Applications d’un corps fini dans lui-même, Thèse de troisième cycle. Université de Rennes, 1984.
- On the cycle structure of repeated exponentiation modulo a prime. J. Number Theory, 107(2):345–356, 2004.
- L. Mirsky. The number of representations of an integer as the sum of a prime and a k-free integer. The American Mathematical Monthly, 56(1P1):17–19, 1949.
- Steve Morgan. The world will store 200 zettabytes of data by 2025. https://cybersecurityventures.com/the-world-will-store-200-zettabytes-of-data-by-2025/, Mar 2021. Accessed 2023-11-01.
- Mathematical Association of America. The 2017 Putnam competition problems and solutions, 2017.
- Connected components of the graph generated by power maps in prime finite fields. Integers, 18A:Paper No. A16, 8, 2018.
- Thomas D. Rogers. The graph of the square mapping on the prime fields. Discrete Mathematics, 148(1-3):317–324, 1996.
- The structure of digraphs associated with the congruence xk≡y(modn)superscript𝑥𝑘annotated𝑦pmod𝑛x^{k}\equiv y\pmod{n}italic_x start_POSTSUPERSCRIPT italic_k end_POSTSUPERSCRIPT ≡ italic_y start_MODIFIER ( roman_mod start_ARG italic_n end_ARG ) end_MODIFIER. Czechoslovak Math. J., 61(136)(2):337–358, 2011.
- On the iteration of certain quadratic maps over GF(p)GF𝑝{\rm GF}(p)roman_GF ( italic_p ). Discrete Math., 277(1-3):219–240, 2004.
Paper Prompts
Sign up for free to create and run prompts on this paper.