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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).
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If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
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