prove that :

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Blazing goIITian

total posts: 2717
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maybe it is wrong..

2n+1 is odd. so let,

$2n+1=(2a+1)^2=4a^2+4a+1\\Rightarrow n=2a(a+1)$

As a(a+1) is even so n is divisible by 4.

Again as n is even 3n+1 is odd. so let

$3n+1=(2b+1)^2=4b^2+4b+1\\\\\Rightarrow 3n=4b(b+1)$

and b(b+1) is even , so n must be divisible by 8.

As we know that every square leaves remainder 0,1,4 when divided by 5, we can say that n is divisible by 5.

As it is divisible by 5 and 8, it must be divisible by 40..

[IMG]http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/6/3/0638cc54ee34d87aa803d78fe3ec072aa8749bf5.gif[/IMG] :)

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