← MATH 01352 · Theory of Numbers
MATH 01352 · Divisibility & primes
Fundamental Theorem of Arithmetic
Definition
Every integer n>1 factors uniquely (up to order) as a product of primes. Uniqueness is the deep part — existence is easier by well-ordering/induction.
Read this
Prime p divides ab ⇒ p|a or p|b (Euclid’s lemma) — key lemma toward uniqueness.
gcd/lcm via min/max of prime exponents.
Applications everywhere: fractions in lowest terms, cryptography setup, radical-simplified roots.
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 3
Click the card to flip
Try this
Attempt each problem first, then open the worked solution.
1.Prove √2 is irrational using unique factorization (standard proof).