PROBLEM OF THE MONTH

February 2003






  1. How many positive integers n\le 10000 there are such that the difference 2^n-n^2 is not divisible by 7?
  2. Find all positive integers $ n$ for which n^{10}+1 is divisible by 10!

Submit your solution to the Mathematics Undergraduate Office (Math P-142) or electronically to Prof. S. Popescu at 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: February 28th at 1 pm.