1.[1911/3] Prove that 3n +1 is not divisible by 2n for any integer n. 2.[1913/1] Prove that for every integer n > 2 (1 x 2 x 3 x …n)2 > nn 3.[1914/1] Let A and B be the points on the circle k. Suppose that an arc l' of another circle l, connects A and B and divides the area inside the circle k into two equal parts. Prove that arc l' is longer then the diameter k. 4.[1922/3] Show that if a1, a2, …, an be n distinct natural numbers, none divisible by any primes greater then 3, then 1/a1 + 1/a2 + … +1/an < 3 Problems will be due on May 15, 2004. Check www.ndsu.edu/math/talent for solutions and more problems! Send your answers, along with this form to: Talent Search, Dept. of Mathematics, NDSU, Fargo, ND 58105. Your Name: __________________________________     Set: 4 Your Address: __________________________________ 1. _____ __________________________________ 2. _____ __________________________________ 3. _____ Your High School: __________________________________ 4. _____ Grade: _____ Total: _____