Difference between revisions of "2017 USAJMO Problems"
Liopleurodon (talk | contribs) (→Problem 6) |
Liopleurodon (talk | contribs) (→Problem 6) |
||
Line 28: | Line 28: | ||
===Problem 6=== | ===Problem 6=== | ||
− | |||
− | |||
{{MAA Notice}} | {{MAA Notice}} | ||
{{USAJMO newbox|year= 2017 |before=[[2016 USAJMO]]|after=[[2018 USAJMO]]}} | {{USAJMO newbox|year= 2017 |before=[[2016 USAJMO]]|after=[[2018 USAJMO]]}} |
Revision as of 19:18, 20 April 2017
Contents
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 the area of triangle .
Day 2
Problem 4
Problem 5
Problem 6
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
2017 USAJMO (Problems • Resources) | ||
Preceded by 2016 USAJMO |
Followed by 2018 USAJMO | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAJMO Problems and Solutions |