Subject Computer Science Discrete Math

Question

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 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...

This is only a preview of the solution. Please use the purchase button to see the entire solution

Assisting Tutor

Related Homework Solutions

Induction Proof Exercises
Homework Solution
$25.00
induction
proof
integer
relationship
polygon
triangles
triangulation
prove
discrete
math
Discrete Math Questions
Homework Solution
$40.00
Discrete Mathematics
Probability
Statistics
Combinations
Permutations
Outcomes
Balls
Replacements
Lists
Dices
Events
Digits
Integers
Odd Numbers
Even Numbers
Rows
Multiplication
Get help from a qualified tutor
Live Chats