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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
Verify the Parseval theorem for the discrete-time signal x(n) and its DFT from given equations. Compute the linear convolution of the discrete-time signal x(n) ={3, 2, 2,1} and
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