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 Post subject: Question?Posted: Thu, 19 Aug 2010 09:22:22 UTC
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Joined: Sat, 27 Mar 2010 13:58:25 UTC
Posts: 30
Location: india,new delhi
Let A1,A2.....An be n numbers such that A2 is either 1 or -1.if A1A2A3A4+A2A3A4A5......+AnA1A2A3=0 then prove that 4 divides n. (1,2... are in base of A)

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 Post subject: Re: Question?Posted: Thu, 19 Aug 2010 10:17:44 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7492
Location: NCTS/TPE, Taiwan
anmol singh wrote:
Let A1,A2.....An be n numbers such that A2 is either 1 or -1.if A1A2A3A4+A2A3A4A5......+AnA1A2A3=0 then prove that 4 divides n. (1,2... are in base of A)

Thought I have seen this question before, possibly on another board. You mean for all , not just .

Spoiler:
Easy to get 2|n. To get 4|n, consider the effect of changing signs on the sum.

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