Number Theory Mind Map

Every number theory visualization on this site on one map. The branches are the main ideas. Each leaf is a page; the grey line under it is the one thing to remember about it. Click a branch to focus on it, click a page to open it.

Recall mode hides the page names. Read the hint, say the name, then click the "?" to check.

1. How the map is organized

Overview of the number theory mind map: Primes and factors, Euclid and GCD, Modular arithmetic, Bits and codes, Number patterns. — The map at a glance: 5 branches, 15 pages.

Ask what the page does with whole numbers:

Does it split a number into building blocks? Finding primes or factors is primes and factors.
Does it work only with remainders? GCD by repeated remainders is Euclid; powers, inverses and systems mod n are modular arithmetic.
Does it store or protect data? Bases, parity bits and polynomials over a finite field are bits and codes.
Does it draw a picture from a simple rule? That is a number pattern.

2. The branches side by side

Branch	Key question	Key tool	Used in
Primes and factors	is n prime? what are its factors?	sieve, factor tree	GCD, LCM, counting divisors
Euclid and GCD	what do a and b share?	a = q·b + r	fractions, modular inverse
Modular arithmetic	what is the remainder?	square and multiply, CRT	RSA, hashing, calendars
Bits and codes	how to store and repair data?	parity, finite fields	ECC memory, RAID-6, QR codes
Number patterns	what shape does a rule make?	spirals, mod N on a circle	open problems, nature

3. Five facts to remember

Every whole number above 1 is a product of primes in exactly one way, up to order.
To test if n is prime, you only need to try divisors up to √n.
Euclid's algorithm is slowest on consecutive Fibonacci numbers, and still takes only O(log n) steps.
a has an inverse mod n exactly when gcd(a, n) = 1.
Square-and-multiply computes bᵉ mod n with about 2·log₂ e multiplications, not e.

See all number theory pages in the index, or the other mind maps.