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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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Consider the equation e x 3 + x 2 - x - 6 = 0, e > 0 (1) 1. Apply a naive regular perturbation of the form do derive a three-term approximation to the solutions
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5 2 ----- - ----- x-1 x+1 -------------------- x 1 ----- + ----- x-1 x+1
Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbles as Sam?
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