PROBLEM NO.39 (B0MC-2,DAY-5)

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SANZEED
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PROBLEM NO.39 (B0MC-2,DAY-5)

Unread post by SANZEED » Wed Apr 04, 2012 10:44 pm

Prove that every integer $n$ can be represented in infinitely many ways as
$n=e.1^{2}+e.2^{2}+....+e.k^{2}$
for a convenient $k$ and a suitable choice for $e$ where $e=\pm1$
Last edited by sourav das on Sat Apr 07, 2012 3:31 pm, edited 1 time in total.
Reason: Use \pm for $\pm$
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

User avatar
SANZEED
Posts:550
Joined:Wed Dec 28, 2011 6:45 pm
Location:Mymensingh, Bangladesh

Re: PROBLEM NO.39 (B0MC-2,DAY-5)

Unread post by SANZEED » Wed Apr 04, 2012 10:49 pm

Hint:
I solved it using induction.
This induction is used to jump from $n$ to $n+k$,($k\ge 2$,then what is $k$?
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

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