Intermediate
Discrete Mathematics & Math
Q60 / 100
What is the Fundamental Theorem of Arithmetic?
Correct! Well done.
Incorrect.
The correct answer is B) Every integer n > 1 has a unique prime factorization (up to order of factors)
B
Correct Answer
Every integer n > 1 has a unique prime factorization (up to order of factors)
Explanation
FTA: n = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ uniquely. Existence (proved by strong induction) and uniqueness (proved using Euclid's lemma: if p|ab and p is prime, then p|a or p|b). Foundation of number theory.
Progress
60/100