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Multiplicative order — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Multiplicative order — a number theory concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Filter by difficulty

These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.

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AMC 10

2018 AMC 10B Problem 13

AMC 12

2016 AMC 12B Problem 22 • 2016 AMC 12B Problem 25 • 2022 AMC 12B Problem 15

AIME

2001 AIME II Problem 10 • 2004 AIME II Problem 10 • 2011 AIME I Problem 11 • 2018 AIME I Problem 11 • 2019 AIME I Problem 14 • 2020 AIME I Problem 12 • 2021 AIME I Problem 14 • 2021 AIME II Problem 9 • 2021 AIME II Problem 13 • 2023 AIME II Problem 15 • 2024 AIME I Problem 13

More number theory concepts

Chicken McNugget TheoremChinese Remainder Theoremcontinued fractiondigitsDiophantine EquationdivisibilityEuler’s Totient Functionfactorfactor countingFermat’s Little Theoremgreatest common divisorleast common multipleLegendre’s Formulamodular arithmeticmodular exponentiationmultiplepalindromeparityperfect powerperfect squarepower of 2primeprime factorizationquadratic residuesum of factorstrailing zerostriangular numberunits digit