MathDB

<span class='latex-italic'>cubic sequence</span>

is a sequence of integers given by

a_n =n^3 + bn^2 + cn + d

, where

b, c

and

d

are integer constants and

n

ranges over all integers, including negative integers.

<span class='latex-bold'>(a)</span>

Show that there exists a cubic sequence such that the only terms of the sequence which are squares of integers are

a_{2015}

and

a_{2016}

<span class='latex-bold'>(b)</span>

Determine the possible values of

a_{2015} \cdot a_{2016}

for a cubic sequence satisfying the condition in part

<span class='latex-bold'>(a)</span>

Problem Statement