Odd and Even Solutions

★ 9/10combinatorics number theory Counting Estimation Casework

Problem

Consider the equation

E:\ x_1 + 2x_2 + 3x_3 + \cdots + nx_n = 2017.

1. Find the largest $n$ for which $E$ has a solution in positive integers $x_1, \dots, x_n$ . 2. Call a positive-integer solution of $E$ odd if $n$ is odd and even if $n$ is even. Prove that the total number of odd solutions equals the total number of even solutions.

Answer

Solution

Difficulty	9/10
Topics	combinatorics, number theory, Counting, Estimation, Casework

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.