MathDB

1

Part of 2005 Hungary-Israel Binational

Problems(2)

right triangle and squares externally drawn

Source: 16-th Hungary-Israel Binational Mathematical Competition 2005

3/29/2007
Squares ABB1A2ABB_{1}A_{2} and BCC1B2BCC_{1}B_{2} are externally drawn on the hypotenuse ABAB and on the leg BCBC of a right triangle ABCABC . Show that the lines CA2CA_{2} and AB2AB_{2} meet on the perimeter of a square with the vertices on the perimeter of triangle ABC.ABC .
geometryperimetergeometric transformationhomothetygeometry unsolved
consecutive positive integers contains exactly 25 primes

Source: 16-th Hungary-Israel Binational Mathematical Competition 2005

3/29/2007
Does there exist a sequence of 20052005 consecutive positive integers that contains exactly 2525 prime numbers?
number theory unsolvednumber theory