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Expert:
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User:
Hello, this is one question with 4 parts. If not possible to answer all please answer part C and DExpert:
I can solve Only D.. do you want it
User:
Okay then, is there another part you can also solve? If yes, please assist also
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helpfulAnswer:
-4+47.k, 3-35.kStep-by-step explanation:
A)
If a = 1, then gcd(1, 3) = 1.
If a > 1, then lets execute a single step of the Euclidean algorithm:
gcd (a+2, a) = gcd(a, (a + 2) mod a)
[Here, "x mod y" denotes the remainder of division of x by y.]
Now, clearly, (a + 2) mod a = 2, since a > 2. (a is
odd, and a 1, so a has to be at least 3.)
So, we have
gcd(a+2, a) = gcd (a, 2).
Continuing with the Euclidean algorithm, we get
gcd(a, 2)= gcd (2, a mod 2).
We know that a is odd, i.e., a mod 2 = 1, and clearly gcd (2, 1) = 1.
D)
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