SOLUTION: For integers a and b show that a|b also equals -a|b and a|-b and -a|-b

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Question 26326: For integers a and b show that
a|b also equals -a|b and a|-b and -a|-b
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
For integers a and b show that
a|b also equals -a|b and a|-b and -a|-b
A|B
HENCE B=M*A WHERE M IS AN INTEGER.
T.P.T.
A|-B...SAY...
WE HAVE FROM B=M*A
-B=-M*A...WHERE -M IS ALSO AN INTEGER
HENCE A|-B....NOTE THE DEFINITION OF PERFECT DIVISION.IT SAYS THAT M HAS TO BE AN INTEGER ONLY.POSITIVE AND NEGATIVE NUMBERS ARE BOTH INTEGERS.SO IT DOES NOT MAKE ANY DIFFERENCE IF M IS PLUS OR MINUS.