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Given: p | q means p divides q 

           q | p means q divides p

proof: Since p divides q then it can be written as q = p*k            where k $\epsilon$ Z 

          so k = $\frac{p }{q}$          --- eq 1 

          and q divides p then it can be represented as p = q*m            where m $\epsilon$ Z 

          so m =   $\frac{q }{p}$         ----eq 2

           from eq 1 and eq 2 it can be said that 

          k = $\frac{1 }{m}$              

          so m * k  = 1 

      now , since m and k are integers and their product is 1 

       hence m = k =1 

       so from eq 1 we can substitute value of k which is 1 

       1= $\frac{p }{q}$ 

       so , q =p                      [hence proved].

 

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