PROBLEM OF THE MONTH

November 2006





Unfortunately, we did not receive any complete, correct solution this month.

Let p1, p2, ... , pn be different primes. Prove that, for any integers a1, a2, ... , an not simultaneously equal to zero, the number

a1 p11/2+ a2 p21/2+ ... + an pn1/2

is nonzero.

This month's prize will be awarded to the best explained, correct solution.



Submit your solution to the Mathematics Undergraduate Office (Math P-142) or electronically to problem@math.sunysb.edu by the due date. Acceptable electronic formats are: PDF, Postscript, DVI, (La)TeX, or just plain text. Please include your name and phone number, or preferably your email address.

Closing date: December 1st at 12 pm.