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Topic: Number with n^3 , 109
Replies: 5   Last Post: Jan 10, 2013 5:42 AM

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William Elliot

Posts: 1,705
Registered: 1/8/12
Re: Number with n^3 , 109
Posted: Jan 1, 2013 9:08 PM
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On Wed, 2 Jan 2013, mina_world wrote:

> n^3 + (n+1)^3 + (n+2)^3 = 57 + 59 + 61 + ... + 109
>

Let k = n + 1.
(k - 1)^3 + k^3 + (k + 1) = 57(111 - 57)/2 + 2 + 4 +..+ 52

3k^3 + 6k = 57*27 + 2(1 + 2 +..+ 26)
3k(k^2 + 2) = 57*27 + 2*26*27/2

k(k^2 + 2) = 57*9 + 26*9 = 83*9; k = 9; n = 8




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