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A. 578. For every integer n2 let P(n) be the product of all expressions of the form where the signs of the terms are chosen arbitrarily.

(a) Prove that P(n) is a positive integer.

(b) Prove that for all >0 there exists an n0 such that for every n>n0 the largest prime divisor of P(n) is smaller than .

(5 points)

Deadline expired on 11 February 2013.

Statistics on problem A. 578.
 10 students sent a solution. 3 points: 2 students. 1 point: 8 students.

• Problems in Mathematics of KöMaL, January 2013

•  Támogatóink: Morgan Stanley