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        riddles >> easy >> Seeing double
        
(Message started by: BenVitale on Dec 31^st, 2009, 4:38am)

Title: Seeing double
Post by BenVitale on Dec 31^st, 2009, 4:38am

Say we have a 3-digit number A = xyz

Is it possible to get a square by writing twice the same natural number?

I mean from A = xyz to B = xyzxyz (now a 6-digit number)

My question is : could we get a number B being a square?

For example,

if A = 123, then B = 123123 is not a square
Similarly if A = 456, B = 456456 : it is not a square.

Title: Re: Seeing double
Post by ThudanBlunder on Dec 31^st, 2009, 4:52am

Consider that B = 1001A = 7*11*13*A

Title: Re: Seeing double
Post by MathsForFun on Jan 1^st, 2010, 3:07am

on 12/31/09 at 04:38:38, BenVitale wrote:

Is it possible to get a square by writing twice the same natural number?

No.

Title: Re: Seeing double
Post by Immanuel_Bonfils on Jan 20^th, 2010, 4:06pm

on 12/31/09 at 04:52:10, ThudanBlunder wrote:

Consider that B = 1001A = 7*11*13*A

Almost: 1002001