Thread: contradiction

hi..how can i prove by contradiction that

that if

p is a prime number and p divides a1a2...an

where ai is an integer for i = 1; 2; 3... n, then p divides jai for some integer i

thank you

Originally Posted by qwerty321

hi..how can i prove by contradiction that

that if

p is a prime number and p divides a1a2...an

where ai is an integer for i = 1; 2; 3... n, then p divides jai for some integer i

thank you

Assume by contradiction. Then . However, . Since and therefore . Similar reasoning shows that and so . Continue down this path until you reach but then , however, . This is a contradiction.