Solution: According to division algorithm, we have n = 6q + r ; 0 ≤ r < 6 Let, A = n(7n2 + 5) For r = 0, we have A = n(7n2 + 5) = (6q + r) {7(6q + r)2 + 5} = 6q (7.36q2 + 5) = ...

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## Assuming that gcd(a, b) = 1 then prove that gcd(2a + b, a + 2b) = 1 or 3

Proof: Let d = gcd(2a + b, a + 2b) Then there exists r and s such that 2a + b = dr and a + 2b = ds Now, 3a = 2(2a + b) –(a + 2b) = 2dr – ds = d(2r- s) And hence d\3a Also, 3b ...

Read More »## Definition of Graph| Discrete mathematics

Graph: A graph is said to be planner if it can be drawn on a plane in such a way that no edges cross one another except of course at common vertices. Finite region and infinite region: A region is said to be finite if it is area is finite ...

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