1
Part of 2008 Hungary-Israel Binational
Problems(2)
Hungary-Israel Binational 2008\1
Source:
11/5/2008
Find the largest value of n, such that there exists a polygon with n sides, 2 adjacent sides of length 1, and all his diagonals have an integer length.
inequalitiestriangle inequalitygeometryperpendicular bisectorgeometry proposed
Hungary-Israel Binational 2008\4
Source: floor function identity
11/5/2008
Prove that: \sum_{i\equal{}1}^{n^2} \lfloor \frac{i}{3} \rfloor\equal{} \frac{n^2(n^2\minus{}1)}{6}
For all .
floor functionalgebra proposedalgebra