2016 JBMO Problems/Problem 3

Problem

Find all triplets of integers $(a,b,c)$ such that the number

is a power of $2016$ .

(A power of $2016$ is an integer of form $2016^n$ ,where $n$ is a non-negative integer.)

It is given that $a,b,c \in \mathbb{Z}$

Let $(a-b) = -x$ and $(b-c)=-y)$ then $(c-a) = x+y$ and $x,y \in \mathbb{Z}$

We can then distinguish between two cases:

Case 1: If $n=0$

Case 2: If $n>0$

2016 JBMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4
All JBMO Problems and Solutions