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Question 26682: Let a not equal 0, b and c be integers with a and b relatively prime.
Show that if a|b*c then a|c.
how do i give equations for relatively prime and divisible and then substitute.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Let a not equal 0, b and c be integers with a and b relatively prime.
Show that if a|b*c
A|BC...HENCE....
BC=A*M......I.......WHERE M IS AN INTEGER
AND B ARE RELATIVELY PRIME...THAT IS THEY HAVE NO COMMON FACTORS OR THEIR GCD IS 1.
HENCE GCD =1 =AX+BY...WHERE X AND Y ARE INTEGERS..MULTIPLYING BY C THROUGHOUT,WE GET..
C=CAX+CBY...SUBSTITUTING EQN.I...
C=CAX+AMY=A(CX+MY)=A*K SAY.....WHERE K=CX+MY...
BUT C,X,M,Y ARE ALL INTEGERS...HENCE K IS AN INTEGER.
C=A*K....OR...A DIVIDES C....A|C
then a|c.
how do i give equations for relatively prime and divisible and then substitute.
USE GCD OF A AND B =XA+YB...TO CONVERT INTO EQNS.HOPE YOU UNDERSTOOD.
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