Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2020 OIM Problems/Problem 2

Revision as of 13:45, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == For each positive integer <math>n</math>, define <math>T_n</math> as the smallest positive integer such that <math>1 + 2 + \cdots + T_n</math> is a multiple of <...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

For each positive integer $n$, define $T_n$ as the smallest positive integer such that $1 + 2 + \cdots + T_n$ is a multiple of $n$. For example, $T_5 = 4$ since $1$, $1 + 2$ and $1 + 2 + 3$ are not multiples of $5$, but $1 + 2 + 3 + 4$ is a multiple of $5$. Find all positive integers $m$ such that $T_m \ge m$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

OIM Problems and Solutions

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2020_OIM_Problems/Problem_2&oldid=207348"