Math & Number Theory

Primes, GCD, modular arithmetic, combinatorics and the overflow traps around them.

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What you actually need to hold in your head

Sieve of Eratosthenes marks composites fast
Euclid reduces gcd(a,b) to gcd(b, a mod b)
Fast exponentiation squares its way to the answer
Watch integer overflow and negative modulo

This unlocks

Bit Manipulation

Next in the path

Design (LLD)

Watch it run

Step through the algorithm before you write it.

Sieve of EratosthenesM

Walk the numbers. The first unmarked number is prime, and all of its multiples are not. Start marking from its square.

O(n log log n)

Patterns in this topic

The trigger phrases are what you are training yourself to notice.

Number Theory ToolkitSieve near linear, others logarithmic

A handful of classic routines cover most of it: sieve, Euclid, fast power and factorisation up to the square root.

primes up to ngcd or lcm