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Legendre’s Formula — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Legendre’s Formula — 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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 8

2017 AMC 8 Problem 19 · 2026 AMC 8 Problem 24

AMC 10

2015 AMC 10B Problem 23 · 2024 AMC 10B Problem 22

AMC 12

2006 AMC 12B Problem 22 · 2017 AMC 12B Problem 16 · 2019 AMC 12A Problem 24 · 2024 AMC 12B Problem 16

AIME

1999 AIME Problem 13 · 2009 AIME II Problem 7 · 2020 AIME I Problem 7

More number theory concepts

Chicken McNugget TheoremChinese Remainder Theoremcontinued fractiondigitsDiophantine EquationdivisibilityEuler’s Totient Functionfactorfactor countingFermat’s Little Theoremgreatest common divisorleast common multiplemodular arithmeticmodular exponentiationmultiplemultiplicative orderpalindromeparityperfect powerperfect squarepower of 2primeprime factorizationsum of factorstrailing zerostriangular numberunits digit