IMO 2020 Shortlist N2
For each prime p, there is a kingdom of p-Landia consisting of p islands numbered 1, 2, ..., p. Two distinct islands num...
Category: Number Theory
Problem
For each prime p, there is a kingdom of p-Landia consisting of p islands numbered
1, 2, ..., p. Two distinct islands numbered n and m are connected by a bridge if and only if
p divides pn2
´ m 1qpm2 ´ n 1q. The bridges may pass over each other, but cannot cross.
Prove that for infinitely many p there are two islands in p-Landia not connected by a chain of
bridges.
(Denmark)