For any natural numbers m,n, and k, such that k divides both m+2n and 3m+4n,k must be a common divisor of
Started 9 months ago by Shashank in
Explanatory Answer
k divides m + 2n
So, k also divides 2(m + 2n) = 2m + 4n
It is given that k divides 3m + 4n
Which means, k should also divide (3m + 4n) – (2m + 4n)
∴k divides m
Since k divides m and m + 2n
k should also divide (m + 2n) – m = 2n
Therefore, k divides m and 2n.
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