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?
(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 20200909 22:58:23 