if α|β and α|ε, then α|(mβ + nε)
smallest positive linear combination of α and β = gcd(α, β)
if gcd(α, ε) = 1 and gcd(β, ε) = 1, then gcd(αβ, ε) = 1
if ε|αβ and gcd(ε, α) = 1, then ε|β
gcd(α, β) = gcd(β, α mod β); why the euclidean algorithm works
if ρ is prime and ρ|αβ, then ρ|α or ρ|β
δ = gcd(α, β) ⇒ 1 = gcd(α/δ, β/δ)
(α ≡ β mod Μ and ε ≡ δ mod Μ) ⇒ α + ε ≡ β + δ mod Μ
(α ≡ β mod Μ and ε ≡ δ mod Μ) ⇒ αε ≡ βδ mod Μ
(αε ≡ βε mod Μ and gcd(ε, Μ) = 1) ⇒ α ≡ β mod Μ
using combinations to find a number in the Pascal's triangle
number of ways of arranging n objects with k identical objects
finding a term in an arithmetic sequence
finding a term in a geometric sequence
the sum of an arithmetic series
the sum of a geometric series with finite terms
the sum to infinity of a geometric series
sum of the first n positive integers
sum of the squares of the first n positive integers
sum of the cubes of the first n positive integers
showing that the harmonic series diverges