If we have a sequence <msubsup> { &#x03B1;<!-- α --> <mrow clas

Jackson Duncan

Jackson Duncan

Answered question

2022-06-26

If we have a sequence { α n } n = 3 such that α n is the least prime divisors of n ! 1
To show:
n = 3 1 α n

Answer & Explanation

ejigaboo8y

ejigaboo8y

Beginner2022-06-27Added 29 answers

Wilson's theorem helps to prove that the sequence diverges : For all integers n > 1 for which n+2 is prime , we have
( n + 2 ) n ! 1
This follows from
( n + 1 ) ! 1 mod ( n + 2 )
and
n + 1 1 mod ( n + 2 )
In this case, the smallest prime factor is obviously n+2
Hence the sum contains all the reciprocals of the primes p 5. Since the sum of the reciprocals of the primes diverges, the claim follows.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?