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AMC number theory problems

Divisibility and primes, modular arithmetic, digits and number bases, and Diophantine equations.

566 problems in the archive use these ideas — 310 from the AMC 10 and 256 from the AMC 12.

Picks a problem you have not seen, at about the difficulty you are handling.

Narrow it down

  • Divisibility & Primes311

    Divisibility, prime factorisation, counting factors, GCD and LCM, and perfect powers.

  • Modular Arithmetic179

    Remainders, congruences, parity, units digits and modular exponentiation.

  • Digits & Number Bases155

    Digit manipulation, place value, number bases, palindromes and repeating decimals.

  • Diophantine Equations58

    Finding the integer solutions of an equation with more unknowns than constraints.

60 most recent problems

Newest contests first. Every problem opens with its answer choices, hints and a worked solution.

Use Start number theory practice above to keep going through the remaining 506, or browse them by contest in the AMC 12 and AMC 10 archives.