Category
Number Theory
Primes, divisibility, and modular arithmetic worth the detour.
Number theory is the study of the integers, and it is where elementary tools go furthest. Divisibility, primes and modular arithmetic settle questions that look far out of reach.
Problems here range from digit puzzles and divisibility arguments up to congruences, Diophantine equations, and orders modulo n. Checking small cases is not cheating — it is usually how the pattern gets found.
Latest problems
137 problems
Matching Divisor Counts
1583
9
Numbers with Three Divisors
1333
12
Perfect Square Factors Count
1095
30
Remainder of a Binomial Coefficient Sum
1333
7
Remainder of a Surd Power Sum
1333
10
Right Triangles with Fixed Hypotenuse
1228
14
Second Smallest Integer Solution to an Equation
1500
10
Smallest Factorial Divisible by a Number
993
47
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