Logo for LIVE by Po-Shen Loh

LIVE

English

Perfect power — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses perfect power — 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

2009 AMC 8 Problem 17 · 2018 AMC 8 Problem 25

AMC 10

2003 AMC 10B Problem 14 · 2007 AMC 10A Problem 17 · 2019 AMC 10A Problem 11

AMC 12

2000 AMC 12 Problem 7 · 2010 AMC 12B Problem 9

AIME

2017 AIME I Problem 13 · 2018 AIME II Problem 3 · 2025 AIME I Problem 15

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 exponentiationmultiplemultiplicative orderpalindromeparityperfect squarepower of 2primeprime factorizationsum of factorstrailing zerostriangular numberunits digit