Difference between revisions of "2016 JBMO Problems/Problem 3"
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== Problem == | == Problem == | ||
| + | Find all triplets of integers <math>(a,b,c)</math> such that the number | ||
| + | <cmath>N = \frac{(a-b)(b-c)(c-a)}{2} + 2</cmath> | ||
| + | is a power of <math>2016</math>. | ||
| + | |||
| + | (A power of <math>2016</math> is an integer of form <math>2016^n</math>,where <math>n</math> is a non-negative integer.) | ||
== Solution == | == Solution == | ||
such that the number
![\[N = \frac{(a-b)(b-c)(c-a)}{2} + 2\]](http://latex.artofproblemsolving.com/4/9/6/496f7460105427895e3c88cb3d99ffadfb21bc41.png)
.
,where 
is a non-negative integer.)
