MathDB
remainder from division sum_{i=1}^{2006} x_i^2 with 2551

Source: Mathcenter Contest / Oly - Thai Forum 2008 R1 p3 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 10, 2022
number theory

Problem Statement

Set M={1,2,⋯ ,2550} M= \{1,2,\cdots,2550\} and min⁡A, max⁡A\min A ,\ \max A represents the minimum and maximum values of the elements in the set AA. For k∈{1,2,⋯2006} k \in \{1,2,\cdots 2006\} define xk=12008(∑A⊂M:n(A)=k( minA+max⁡A) ) x_k = \frac{1}{2008} \bigg (\sum_{A \subset M : n(A)= k} (\ min A + \max A) \, \bigg) . Find remainder from division ∑i=12006xi2\sum_{i=1}^{2006} x_i^2 with 25512551.
(passer-by)
Back to ProblemsView on AoPS