Mathematical and Physical Journal
for High Schools
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Problem A. 578. (January 2013)

A. 578. For every integer n\ge2 let P(n) be the product of all expressions of the form \pm\sqrt1 \pm\sqrt2 \pm\sqrt3 \pm\ldots \pm\sqrt{n} where the signs of the terms are chosen arbitrarily.

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

(b) Prove that for all \varepsilon>0 there exists an n0 such that for every n>n0 the largest prime divisor of P(n) is smaller than 2^{2^{\varepsilon n}}.

(5 pont)

Deadline expired on February 11, 2013.


10 students sent a solution.
3 points:2 students.
1 point:8 students.

Problems in Mathematics of KöMaL, January 2013