SOLUTION: Could you please help me prove the following mathematical statement. Let p be a prime number and a and b positive integers, such that p/ab. then p/a or p/b.

Question 870785: Could you please help me prove the following mathematical statement.
Let p be a prime number and a and b positive integers, such that p/ab. then p/a or p/b.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
If p | a, we are done.

Otherwise, p and a are relatively prime, so by Bezout's identity, there exist integers m and n such that pm + an = 1. Multiplying both sides by b, pmb + abn = b. Since pmb and abn are divisible by p (p | ab), then the sum pmb + abn is divisible by p, so b is divisible by p.
RELATED QUESTIONS
Let n be a positive integer, k the number of prime numbers less than or equal to n, and... (answered by richard1234)

Use the binomial theorem and mathematical induction to show the following. Let p be a... (answered by khwang)

Prove or disprove the following: The expression n2 � n +41 produces a prime number for... (answered by richard1234)

Let P(n) be the statement that 3^1 + 3^2 + � � � 3^n = 3/2(3^n-1) for the positive... (answered by ikleyn)

Let G be a group and let a b be some elements of G. Prove or disprove the following... (answered by jorel1380)

Please help me with this mathematical induction question: Suppose we want to use... (answered by ikleyn)

Please help me solve and explain how to solve this mathematical induction: Use... (answered by Edwin McCravy)

let k be an integer and p is a prime such that the quadratic equation x^2+kx+p=0 has two... (answered by ankor@dixie-net.com)

Let a and b be positive integers, assume that (a^(3))|(b^(3)). How do i prove tha a|b (answered by venugopalramana)