Hi plz give me a help to find the answer for following
If , gcd(a,b)=g and is a solution of then show that ,
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Originally Posted by dhammikai Hi plz give me a help to find the answer for following
If , gcd(a,b)=g and is a solution of then show that , Here we are dealing with integer solution of
Since, is a solution
Since there are infinite integer solution(why?), let us introduce an integer parameter m such that
Now, to ensure that RHS is always an integer, make substitution ....where t is new integer parameter.
(1) ax + by = c
(2) is an integer solution.
Subtracting (2) from (1), .
Thus . But therefore, . Hence it follows that there is a such that
(3) . Substituting this in (*), . Hence
Therefore, from above and (3),
OK Thanks, I got the idea for the answer, thanks again
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