MathDB

3

Part of 2001 Irish Math Olympiad

Problems(2)

identity

Source: Ireland 2001

7/5/2009
Show that if an odd prime number p p can be expressed in the form x^5\minus{}y^5 for some integers x,y, x,y, then: \sqrt{\frac{4p\plus{}1}{5}}\equal{}\frac{v^2\plus{}1}{2} for some odd integer v v.
number theory proposednumber theory
easy exercise

Source: Ireland 2001

7/5/2009
In an acute-angled triangle ABC ABC, D D is the foot of the altitude from A A, and P P a point on segment AD AD. The lines BP BP and CP CP meet AC AC and AB AB at E E and F F respectively. Prove that AD AD bisects the angle EDF EDF.
geometry proposedgeometry