 # Discrete Mathematics Problem

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

## Related Homework Solutions

Prime Numbers, Numeration Bases & Euclidean Algorithm \$18.00
GCD
Euclidean Algorithm
Prime
Base
Division
Binary
Octal
Computer Science
Discrete Math
Induction Proof Exercises \$25.00
induction
proof
integer
relationship
polygon
triangles
triangulation
prove
discrete
math
Master Theorem & Recurrence Relations Exercises \$8.00
Master
Theorem
Recurrence
Relation
Big
Theta
Induction
Recursive
Bounded
Constant
Factor
Floor
Questions Involving Functions: One-to-one, Onto, Inverse, Composition, Examples \$30.00
Question
Function
One-to-one
Onto
Map
Inverse
Compose
Identity
Rule
Counterexample
Real
Projection
Coordinate
Set
Diagram
Discrete Math Questions \$40.00
Discrete Mathematics
Probability
Statistics
Combinations
Permutations
Outcomes
Balls
Replacements
Lists
Dices
Events
Digits
Integers
Odd Numbers
Even Numbers
Rows
Multiplication
Divisibility Proof: Discrete Math \$3.00
divisible
mod
even
odd
sum
multiple
remainder
expression
integer
proof
discrete
divisibility
Live Chats