MathDB

1

Part of 2008 ITAMO

Problems(2)

Italian Mathematical Olympiad 2008

Source: Problem 1

8/23/2008
Let ABCDEFGHILMN ABCDEFGHILMN be a regular dodecagon, let P P be the intersection point of the diagonals AF AF and DH DH. Let S S be the circle which passes through A A and H H, and which has the same radius of the circumcircle of the dodecagon, but is different from the circumcircle of the dodecagon. Prove that: 1. P P lies on S S 2. the center of S S lies on the diagonal HN HN 3. the length of PE PE equals the length of the side of the dodecagon
geometrycircumcirclegeometry proposed
Italian Mathematical Olympiad 2008

Source: Problem 4

8/23/2008
Find all triples (a,b,c) (a,b,c) of positive integers such that a^2\plus{}2^{b\plus{}1}\equal{}3^c.
number theory proposednumber theory