Midterm Number Theory

Front 1

Goldbach Conjecture

Back 1

Every even number greater than or equal to 2 is the sum of 2 primes

Front 2

Twin Prime Conjecture

Back 2

them are infinitely many prime pairs that are 2 units apart

Front 3

Defn of prime number

Back 3

n greater than 1, must always be positive, and its only factors be +1 and n.

Front 4

Prime Number Theorem

Back 4

pi(x)= X÷ (ln x)

pi(x) : # of primes less than or = to ×

Front 5

Corollary Prime Num. Theorem

Back 5

Pn= n* ln (n)

Pn: nth prime

Front 6

Bounded Gaps Theorem

Back 6

There exists a constant K s.t. there are infinitely many pairs of primes, p less than q, with q-p <= K.

Front 7

Division Algorithm

Back 7

If a and b are integers w/ b>0, then there are unique integers q(quotient) and r(remainder) s.t. a= qb+r and 0<= r<b

Front 8

Greatest Common Divisor

Back 8

If a and b aren't both 0, the gcd, denoted as (a, b), is a member d that satisfies:

l. d|a and d|b and

2. if c|a and c|b, then c <= d

Front 9

Corollary of gcd & lcm

Back 9

(a,b) * [a,b] = ab

Front 10

a (cong) b (mod m)

Back 10

m| (a-b)

(a-b) = mk

Front 11

X is inverse of a (mod m)

Back 11

ax (cong) 1 (mod m)