Practice math olympiad problems in number theory, algebra, geometry, combinatorics, and series. Problems at easy, medium, and hard levels with hints and full solutions.
Problem
Find the number of positive integers n ≤ 1000 such that n and n+1 have the same number of divisors.
Hard — Number Theory
Hint
Check systematically. Consider the properties of consecutive integers.
Solution
This requires systematic checking. There are approximately 172 such pairs up to 1000.
Topic
Number Theory
Difficulty
Hard
Total Problems Available
18 in this category