arithmetic sequence with infinite terms perfect cubes
Source: Netherlands - Dutch NMO 1967 p2
January 31, 2023
perfect cubenumber theoryarithmetic sequence
Problem Statement
Consider arithmetic sequences where all terms are natural numbers. If the first term of such a sequence is , prove that that sequence contains infinitely many terms that are the cube of a natural number. Give an example of such a sequence in which no term is the cube of a natural number and show the correctness of this example.