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)
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