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Omni-MATH / Find all triplets of integers (a,b,c) such that the number

Problem

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

problem

Find all triplets of integers

(a,b,c)

such that the number

N = \frac{(a-b)(b-c)(c-a)}{2} + 2

is a power of

2016

. (A power of

2016

is an integer of form

2016^n

,where

n

is a non-negative integer.)

Plain-text mathematical notation (without MathML)

Find all triplets of integers (a,b,c) such that the number
N=((a−b)(b−c)(c−a))/(2)+2 
is a power of 2016 .
(A power of 2016 is an integer of form 2016^(n) ,where n is a non-negative integer.)

Original LaTeX notation

Find all triplets of integers $(a,b,c)$ such that the number
\[N = \frac{(a-b)(b-c)(c-a)}{2} + 2\] 
is a power of $2016$ .
(A power of $2016$ is an integer of form $2016^n$ ,where $n$ is a non-negative integer.)

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Source and history

task_id: 28895e10-f4e8-516c-8ce7-27a7ae3c698a
task_key: test--28895e10-f4e8-516c-8ce7-27a7ae3c698a
task_revision_id: 2
config / split: / test

Official source

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