SOLUTION: Dealing with contradiction: Show that for any positive integer a and any prime p, if p is divides a, then p does not divide a+1.

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Question 32755: Dealing with contradiction: Show that for any positive integer a and any prime p, if p is divides a, then p does not divide a+1.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
P|A...SO A=P*M....WHERE M IS AN INTEGER
FOR P TO DIVIDE A+1...
P|PM+1...IMPLIES
(PM+1)/P IS AN INTEGER...THAT IS M+(1/P)IS AN INTEGER...THAT IS 1/P IS
AN INTEGER...THIS IS NOT POSSIBLE AS 1 HAS NO DIVIDERS EXCEPT IT SELF
AND P BEING A PRIME NUMBER DIFFERENT FROM 1 CANNOT DIVIDE 1.