MathDB

2012 Spring CHMMC Tiebreaker 1 - sum x_i^2 = k for nonnegative integers

Source:

March 1, 2024

number theorycombinatoricsCHMMC

Problem Statement

Let

a_k

be the number of ordered

10

-tuples

(x_1, x_2, ..., x_{10})

of nonnegative integers such that

x^2_1+ x^2_2+ ... + x^2_{10} = k.

Let

b_k = 0

a_k

is even and

b_k = 1

a_k

is odd. Find

\sum^{2012}_{i=1} b_{4i}