QuestionQuestion

Suppose that p is a prime number, a and b are integers, and p divides both ab and a + b. Prove that p divides both a and b

This can be used for proving above:
For all primes p and all integers a, b, if p | ab, then p | a or p | b (or both)

Solution PreviewSolution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Given that p divides ab then either a or b or both are multiple of p.
(a) Case 1 : a is multiple of p i.e. there is some integer m such that a = pm
and p divides a + b then...
$10.00 for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

Find A Tutor

View available Discrete Math Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

Decision:
Upload a file
Continue without uploading

SUBMIT YOUR HOMEWORK
We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

  • 1
  • 2
  • 3
Live Chats