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OlympiadBench / 1645 / A cubic sequence is a sequence of integers given by a_(n)=n³+bn²+cn+d,…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Numerical

is multiple answer

false

language

English

question

A cubic sequence is a sequence of integers given by

a_{n}=n^{3}+b n^{2}+c n+d

, where

b, c

and

d

are integer constants and

n

ranges over all integers, including negative integers. Determine the possible values of

a_{2015} \cdot a_{2016}

for a cubic sequence satisfying the condition in part (a).

Plain-text mathematical notation (without MathML)

A cubic sequence is a sequence of integers given by a_(n)=n³+bn²+cn+d, where b,c and d are integer constants and n ranges over all integers, including negative integers.

Determine the possible values of a₂₀₁₅⋅a₂₀₁₆ for a cubic sequence satisfying the condition in part (a).

Original LaTeX notation

A cubic sequence is a sequence of integers given by $a_{n}=n^{3}+b n^{2}+c n+d$, where $b, c$ and $d$ are integer constants and $n$ ranges over all integers, including negative integers.

Determine the possible values of $a_{2015} \cdot a_{2016}$ for a cubic sequence satisfying the condition in part (a).

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1645
task_id: 7340fb93-2cca-5aae-abc7-b9cc914785f7
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1645
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import