MathDB
difference a_{n+1} - a_n is a prime or the square of a prime

Source: Austrian Polish 1989 APMC

April 30, 2020
SequenceprimePerfect Squarenumber theory

Problem Statement

A sequence (an)n∈N(a_n)_{n \in N} of squares of nonzero integers is such that for each nn the difference an+1−ana_{n+1} - a_n is a prime or the square of a prime. Show that all such sequences are finite and determine the longest sequence.
Back to ProblemsView on AoPS