Difference between revisions of "2011 JBMO Problems"
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==Problem 2== | ==Problem 2== | ||
− | Find all primes <math>p</math> such that there exist positive integers <math>x,y</math> that satisfy <math>x(y^2-p)+y(x^2-p)=5p</math> | + | Find all primes <math>p</math> such that there exist positive integers <math>x,y</math> that satisfy <math>x(y^2-p)+y(x^2-p)=5p</math>. |
[[2011 JBMO Problems/Problem 2|Solution]] | [[2011 JBMO Problems/Problem 2|Solution]] |
Latest revision as of 19:52, 2 April 2019
Problem 1
Let be positive real numbers such that . Prove that:
Problem 2
Find all primes such that there exist positive integers that satisfy .
Problem 3
Let be a positive integer. Equilateral triangle ABC is divided into smaller congruent equilateral triangles (with sides parallel to its sides). Let be the number of rhombuses that contain two small equilateral triangles and the number of rhombuses that contain eight small equilateral triangles. Find the difference in terms of .
Problem 4
Let be a convex quadrilateral and points and on sides such that
If is the area of show that
See Also
2011 JBMO (Problems • Resources) | ||
Preceded by 2010 JBMO Problems |
Followed by 2012 JBMO Problems | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |