Consider the following theorem and proof Theorem.There are infinitely many prime
ID: 3209710 • Letter: C
Question
Consider the following theorem and proof Theorem.There are infinitely many primes. ProofSuppose that there exist only finitely many primes p1p2pr. Let N p1 P2.. pr. The integer N-1, being a product of primes, has a prime divisor pi in common with N; so, pi divides N-(N-1) =1, which is absurd! Therefore, there must be infinitely many primes. The phrase that states " the integer N-1 being a product of primes" is justified by which of the following? O The fundamental theorem of arithmetic O The distributive property of arithmetic. O The composite number property of arithemetic. The greatest common divisor property.Explanation / Answer
The fundamental theorem of arithmetic justifies the following statement. It states that every integer greater than 1 has a unique prime factorization.