# SOLUTION: 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.

Algebra ->  Algebra  -> Distributive-associative-commutative-properties -> SOLUTION: 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.      Log On

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 Algebra: Distributive, associative, commutative properties, FOIL Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Distributive-associative-commutative-properties 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.