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

2005 OIM Problems/Problem 4

Revision as of 16:17, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Given two positive integers <math>a</math> and <math>b</math>, <math>a\nabla b</math> denotes the remainder obtained by dividing <math>a</math> by <math>b</math>...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Given two positive integers $a$ and $b$, $a\nabla b$ denotes the remainder obtained by dividing $a$ by $b$. This remainder is one of the numbers $0, 1, \cdots , b - 1$. Find all the pairs of numbers $(a, p)$ such that $p$ is prime and it holds that

\[(a\nabla p)+(a\nabla 2p)+(a\nabla 3p)+(a\nabla 4p)=a+p\]

~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=2005_OIM_Problems/Problem_4&oldid=207474"