13 terms

chapter 3 - Greek number theory

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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