MathDB

1

Part of 2006 Hungary-Israel Binational

Problems(2)

Hungary-Israel Binational 2006_1

Source:

10/27/2008
If natural numbers x x, y y, p p, n n, k k with n>1 n > 1 odd and p p an odd prime satisfy x^n \plus{} y^n \equal{} p^k, prove that n n is a power of p p.
modular arithmeticinductionnumber theory unsolvednumber theory
Hungary-Israel Binational 2006_4

Source:

10/27/2008
A point P P inside a circle is such that there are three chords of the same length passing through P P. Prove that P P is the center of the circle.
quadraticsgeometrypower of a pointgeometry unsolved