This problem first appeared at WXC, and I solved it using an idea I got from 野菜花's 北京初中数学竞赛题. She suggested me to post it here. So here it is. www.ddhw.com The repeat of a positive integer is obtained by writing it twice in a row (so, for example, the repeat of 254 is 254254). Is there a positive integer whose repeat is a perfect square? Because a computer can solve the problem quicker than us, I would add a little flavor to it. a) What is the general format of such numbers? b) Without using a computer, what is the smallest such number you can find? (I will post the smallest one I found.) www.ddhw.com
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