Difference between revisions of "2007 JBMO Problems"
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[[2007 JBMO Problems/Problem 4|Solution]] | [[2007 JBMO Problems/Problem 4|Solution]] | ||
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==See Also== | ==See Also== | ||
{{JBMO box|year=2007|before=[[2006 JBMO]]|after=[[2008 JBMO]]|five=}} | {{JBMO box|year=2007|before=[[2006 JBMO]]|after=[[2008 JBMO]]|five=}} | ||
Revision as of 17:02, 26 February 2024
Problem 1
Let 
be positive real number such that 
. Prove that the equation 
has no real solution.
Problem 2
Let 
be a convex quadrilateral with 
, 
and 
. The diagonals and intersect at point 
. Determine the measure of 
.
Problem 3
Given are 
points in the plane, no three of them belonging to a same line. Each of these points is colored using one of four given colors. Prove that there is a color and at least 
scalene triangles with vertices of that color.
Problem 4
Prove that if 
is a prime number, then 
is not a perfect square.
Solution dddddddd
See Also
| 2007 JBMO (Problems • Resources) | ||
| Preceded by 2006 JBMO |
Followed by 2008 JBMO | |
| 1 • 2 • 3 • 4 | ||
| All JBMO Problems and Solutions | ||
