VIP Exclusive
IMO International Mathematics Olympiad VIP Practice Exam
IMO — The International Mathematical Olympiad (IMO), organized annually by the International Mathematical Union (IMU) since 1959, consists of 6 proof-based problems over 2 days (4.5 hours per day, 3 problems per day) covering algebra, combinatorics, geometry, and number theory; problems are scored 0–7 each (42 points total) with no multiple-choice component — this practice exam adapts those four core domains into a scored MCQ format at comparable difficulty.
30
Questions
90m
Time Limit
75.00%
To Pass
Question 1 of 30👑 VIP
For which positive integers n is it true that n divides (2ⁿ − 1)? A student claims that by Fermat's Little Theorem, every prime p divides 2^(p−1) − 1, so surely many primes satisfy n | (2ⁿ − 1). Investigate: among n = 1, 2, 3, 5, 7, which values actually satisfy n | (2ⁿ − 1)?
Questions 2–30 and full explanations are VIP-exclusive.