a ≡ b (mod m) =⇒ a ≡ b (mod 2m) |
(1) |
a ≡ b (mod 2m) =⇒ a ≡ b (mod m) |
(2) |
(a) (3 points) Is statement (1) true or false? Prove or disprove it. (b) (3 points) Is statement (2) true or false? Prove or disprove it.
O(·).
Use mathematical induction to prove that
H_{1 }+ H_{2 }+ ··· + H_{n }= (n + 1)H_{n }− n.
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