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Number Theory
The mathematics of whole numbers. Some of the oldest problems and the newest cryptography live here: factor a number into primes, run Euclid's algorithm, compute huge powers modulo a prime without ever writing the power down.
Lezioni
Introductory
Prime factorisation
Every integer is a product of primes in exactly one way.
prime factorization of 360
Introductory
Prime numbers
Testing for primality by trial division up to the square root.
is 97 prime
Introductory
GCD and LCM
Euclid's algorithm and the identity gcd × lcm = a × b.
gcd(48, 18)
Core
Modular arithmetic
Remainders, congruences, fast powers and modular inverses.
3^100 mod 7
Introductory
Divisors
Counting and listing divisors from the prime factorisation.
divisors of 36
Core
Sequences
Fibonacci, recurrences and closed forms.
fib(20)
Introductory
Number bases
Converting between decimal, binary, octal and hexadecimal.
255 to binary
Altri rami
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