Monday, 26 September 2016

number theory - Prove that for any integer k>1 and any positive integer n, there exist n consecutive odd integers whose sum is nk

Found these problems in a problem book and got stuck. The book doesn't have solutions to I've come here for help.



(1) Prove that for any integer k>1 and any positive integer n, there exist n consecutive odd integers whose sum is nk.



(2) Let n be a positive integer and m any integer of the same parity as n. Prove that there exist n consecutive odd integers whose sum is mn.

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