number theory
Units digit — AMC & AIME Problems
32 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Units digit — 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: Multiplicative Cycles b, b², b³, ... (mod N) and Order.
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.
AMC 8
AMC 10
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
- Legendre’s Formula
- 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