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Repeating squares (Posted on 2020-09-09) Difficulty: 3 of 5
A repeating number is a number such that the first half of the digits are the same as the second half of the digits. For example, 2020 is a repeating number. What is the smallest repeating number that is also a square?

No Solution Yet Submitted by Math Man    
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re(2): Solution | Comment 3 of 5 |
(In reply to re: Solution by Brian Smith)

Ah.  I wasn't sure if I had the smallest one, and obviously I hadn't.
From Sloan's A092118, it looks like the smallest one, the real solution, is:   1322314049613223140496
which is
11 * 11 * 23 * 4093 * 8779 * 23 * 4093 * 8779 * 16
I only had to multiply by 16 rather than 100 to get to 22 digits.

In fact the first 7 numbers in that Sloane series are
11 * 11 * 23 * 4093 * 8779 * 23 * 4093 * 8779  times
4^2, 5^2, 6^2, 7^2, 8^2, 9^2, 10^2
these are all 22 digits.

The 8th number in the series has 42 digits

Edited on September 9, 2020, 11:05 pm
  Posted by Larry on 2020-09-09 22:58:23

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