IMO 1988 LL INA43
(a) The polynomial x2k + 1 + (x+ 1)2k is not divisible by x2 +x+ 1. Find
IMO 1988 LL INA43
Origin: INA
Problem
(a) The polynomial x2k + 1 + (x+ 1)2k is not divisible by x2 +x+ 1. Find the value of k. (b) If p, q, and r are distinct roots of x3 −x2 + x −2 = 0, find the value of p3 + q3 + r3. (c) If r is the remainder when each of the numbers 1059, 1417, and 2312 is divided by d, where d is an integer greater than one, find the value of d −r. (d) What is the smallest positive odd integer n such that the product of 21/7, 23/7, . . . , 2(2n+1)/7 is greater than 1000?