Integer sequence containing square numbers
Source: Austrian Regional Competition for Advanced Students 2012, #3
May 23, 2012
modular arithmeticarithmetic sequencealgebra proposedalgebra
Problem Statement
In an arithmetic sequence, the di fference of consecutive terms in constant. We consider sequences of integers in which the di fference of consecutive terms equals the sum of the differences of all preceding consecutive terms.
Which of these sequences with and 1\leqslant d = a_1-a_0 \leqslant 43 contain square numbers?