Number theory
Divisibility181 problems · 11 skills
Assorted divisibility puzzles 15Counting multiples 18🔒Divisibility by 11 18🔒Divisibility by 3, 4 and 6 18🔒Divisibility by 7 and 13 10🔒Divisibility by 9 and 99 18🔒Largest divisors 18🔒Largest multiple below a bound 13🔒Missing digits for divisibility 18🔒Mixed divisibility conditions 18🔒Multiples with digit conditions 17🔒
Divisors119 problems · 8 skills
Divisors and common divisors 18Divisors of special numbers 18🔒Extremes of divisors 15🔒Factor pairs 11🔒Listing factors 3🔒Number and product of divisors 18🔒Numbers with a given divisor count 18🔒Sums of divisors 18🔒
Primes and factorisation94 problems · 6 skills
Prime factorisation 18Prime factors of large numbers 18🔒Prime patterns 17🔒Prime solutions of equations 18🔒Runs of composites 5🔒Sums and products of primes 18🔒
GCD and LCM124 problems · 9 skills
Common factors 11Euclid's algorithm 5🔒Extremes with GCD 10🔒GCD of expressions 11🔒Greatest common divisor 18🔒HCF and LCM together 16🔒Least common multiple 18🔒Numbers from HCF and LCM 17🔒Smallest common multiple 18🔒
Remainders101 problems · 6 skills
Numbers with given remainders 18Quotient and remainder 17🔒Remainders of powers 18🔒Remainders of products 18🔒Remainders of recursive sequences 12🔒Remainders of sums 18🔒
Congruences and modular arithmetic127 problems · 8 skills
Chinese remainder theorem 12Ciphers and RSA 15🔒Euler's totient 18🔒Linear congruences 18🔒Modular inverses 17🔒Polynomial congruences 17🔒Quadratic residues and primitive roots 13🔒Residues of powers and factorials 17🔒
Diophantine equations87 problems · 6 skills
Equations with powers 18🔒Frobenius coin problem 9🔒Integer solutions of symmetric equations 17🔒Linear Diophantine equations 15🔒Pell and reciprocal equations 10🔒Powers of 2 and 3 18🔒
Perfect squares and cubes125 problems · 8 skills
Making a perfect cube 17🔒Perfect cubes 13🔒Perfect powers and growth 5🔒Square divisors and square-free numbers 18🔒Square factors and multipliers 18🔒Squares between bounds 18🔒Sums of cubes 18🔒When is it a perfect square? 18🔒
Digits220 problems · 13 skills
Cryptarithms 16🔒Digit counts and leading digits 16🔒Digit sum relations 17🔒Digit sums and carries 17🔒Digit sums over ranges 18🔒Digits in page numbers 12🔒Extremes with digit conditions 18🔒Largest and smallest arrangements 18🔒Moving digits 18🔒Numbers from digit conditions 17🔒Palindromes 18🔒Reversing digits 18🔒Squares with digit conditions 17🔒
Last digits110 problems · 7 skills
Digits of factorials 14🔒Last digit of sums 17🔒Last digits of factorial sums 10🔒Last digits of powers 18🔒Last digits of squares 17🔒Powers with special endings 16🔒Trailing zeros of factorials 18🔒
Number bases78 problems · 5 skills
Arithmetic in other bases 18🔒Base conversion 18🔒Binary and base puzzles 7🔒Finding an unknown base 18🔒Sums of powers of 2 and 3 17🔒
Factorials36 problems · 2 skills
Factorial equations 18🔒Prime powers in factorials and binomials 18🔒
Floor and fractional parts53 problems · 3 skills
Floor and ceiling 18🔒Integer parts of roots 17🔒Sums of floors 18🔒