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each natural number factors into primes in exactly one way

unique prime factorization

x2 - Ny2 = 1 integer solutions are sought

Pell's equation

equations for which integer or rational solutions are sought

diophantine

between 150 and 350 CE Alexandria, used many methods to solve quadratic and cubic Diophantine equations

Diophantus

numbers with no rectangular representation, having no divisors except for 1 and itself, has only a linear representation

prime number

a number that equals the sum of its divisors (including 1 but excluding itself), 6=1+2+3

prefect number

primes of the form 2n-1

Mersenne primes

primes of the form 22n+1

Fermat primes

used to find the greatest common divisor (gcd) of two positive integers a, b

Euclidean algorithm

if p is a prime that divides ab, then p divides a or b

prime divisor property

each positive integer has a unique factorization into primes

fundamental theorem of mathematic

an operation in which the Euclidean algorithm is applied to line segments

anthyphairesis

1801, speaks of the Euclidean algorithm as the "continued fraction algorithm"

Gauss