Difference between revisions of "2017 USAJMO Problems"
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Revision as of 18:02, 19 April 2017
Contents
[hide]Day 1
Note: For any geometry problem whose statement begins with an asterisk (), the first page of the solution must be a large, in-scale, clearly labeled diagram. Failure to meet this requirement will result in an automatic 1-point deduction.
Problem 1
Prove that there are infinitely many distinct pairs of relatively prime positive integers
and
such that
is divisible by
.
Problem 2
Consider the equation
(a) Prove that there are infinitely many pairs of positive integers satisfying the equation.
(b) Describe all pairs of positive integers satisfying the equation.
Problem 3
() Let
be an equilateral triangle and let
be a point on its circumcircle. Let lines
and
intersect at
; let lines
and
intersect at
; and let lines
and
intersect at
. Prove that the area of triangle
is twice that of triangle
.