O Prove the following statements Use a to prove b to prove c a If...

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O Prove the following statements Use a to prove b to prove c a If a b are relatively prime and a b both divide c then ab c Hint use Q2 of HW2 b For nonzero integers d dn define lcm d dn as the smallest positive integer divisible by each d If d dn are pairwise relatively prime then d dn lcm d dn Hint induction on n may be useful c In the setup of the Chinese Remainder Theorem if x Z is a particular solution then x E Z is also a solution if and only if x x mod M where M d dn Hint Show that d must divide x x for each i

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O Prove the following statements Use a to prove b to prove c a If a b are relatively prime and a b both divide c then ab c Hint use Q2 of HW2 b For nonzero integers d dn define lcm d dn as the smallest positive integer divisible by each d If d dn are pairwise relatively prime then d dn lcm d dn Hint induction on n may be useful c In the setup of the Chinese Remainder Theorem if x Z is a particular solution then x E Z is also a solution if and only if x x mod M where M d dn Hint Show that d must divide x x for each i