Question

Let p1 = 2, p2 = 3, . . . , pn be the first n primes, and suppose that N = p1p2p3 . . . pn. If N = ab for some integers a, b, prove that a + b is divisible by a prime greater than pn. Comment on how this result can be used to prove that there are an infinite number of primes

Name: let p1 2 p2 3 pn be the first n primes and suppose that n p1p2p3 pn if n ab for some integers a b prove that a b is divisible by a prime greater than pn comment on how this result can be use 75839
Uploaded: 2022-10-01T05:02:06-08:00
Duration: 5 min 46 s
Channel: Adi S
Description: let p1 2 p2 3 pn be the first n primes and suppose that n p1p2p3 pn if n ab for some integers a b prove that a b is divisible by a prime greater than pn comment on how this result can be use 75839

          Let p1 = 2, p2 = 3, . . . , pn be the first n primes, and
suppose that N = p1p2p3 . . . pn. If N = ab for some integers a, b,
prove that a + b is divisible by a prime greater than pn. Comment
on how this result can be used to prove that there are an infinite
number of primes

Added by Stephen V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

10/01/2022

Step 1

.. * pn and b = pr+1 * pr+2 * ... * ps, where p1, p2, ..., pn are distinct prime numbers. ** Show more…

Show all steps

Thanks for your feedback!

Let p1 = 2, p2 = 3, . . . , pn be the first n primes, and suppose that N = p1p2p3 . . . pn. If N = ab for some integers a, b, prove that a + b is divisible by a prime greater than pn. Comment on how this result can be used to prove that there are an infinite number of primes