Difference between revisions of "2016 JBMO Problems"
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==Problem 3== | ==Problem 3== | ||
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+ | 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.) | ||
[[2016 JBMO Problems/Problem 3#Solution|Solution]] | [[2016 JBMO Problems/Problem 3#Solution|Solution]] |
Revision as of 00:44, 23 April 2018
Contents
[hide]Problem 1
A trapezoid (,) is circumscribed.The incircle of the triangle touches the lines and at the points and ,respectively.Prove that the incenter of the trapezoid lies on the line .
Problem 2
Let be positive real numbers.Prove that
.
Problem 3
Find all triplets of integers such that the number
is a power of .
(A power of is an integer of form ,where is a non-negative integer.)
Problem 4
See also
2016 JBMO (Problems • Resources) | ||
Preceded by 2015 JBMO Problems |
Followed by 2017 JBMO Problems | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |