MathDB
BMT 2022 General p20

Source:

September 28, 2023
number theory

Problem Statement

The game Boddle uses eight cards numbered 6,11,12,14,24,47,546, 11, 12, 14, 24, 47, 54, and nn, where 0n560 \le n \le 56. An integer D is announced, and players try to obtain two cards, which are not necessarily distinct, such that one of their differences (positive or negative) is congruent to DD modulo 5757. For example, if D=27D = 27, then the pair 2424 and 5454 would work because 24542724 - 54 \equiv 27 mod 5757. Compute nn such that this task is always possible for all DD.