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Gửi lúc - 14/07/2002 : 21:48:14
I have some problems for you:
Problem1: In the triangle ABC, the midpoints of AC and AB are M and N respectively. BM and CN meet at P. Show that if it is possible to inscribe a circle in the quadrilateral AMPN (touching every side), then ABC is isosceles.
Define the sequence p1, p2, p3, ... as follows. p1 = 2, and pn is the largest prime divisor of p1p2 ... p(n-1) + 1. Prove that 5 does not occur in the sequence