number theory
Legendre’s Formula — AMC & AIME Problems
13 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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: p-Adic Valuation of a Factorial (Legendre's Formula).
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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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.
AMC 12
More number theory concepts
- Chicken McNugget Theorem
- Chinese Remainder Theorem
- Continued fraction
- Digits
- Diophantine Equation
- Divisibility
- Euler’s Totient Function
- Factor
- Factor counting
- Fermat’s Little Theorem
- Greatest common divisor
- Least common multiple
- Modular arithmetic
- Modular exponentiation
- Multiple
- Multiplicative order
- Palindrome
- Parity
- Perfect power
- Perfect square
- Power of 2
- Prime
- Prime factorization
- Quadratic residue
- Sum of factors
- Trailing zeros
- Triangular number
- Units digit