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Square after square creates a new square (Posted on 2018-12-05) Difficulty: 3 of 5
49 and 1681 are squares with an even number of digits, where both halves are squares, and no zeroes are used.
List all such numbers below 10^10.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts supplement containing non-trivializing zeros | Comment 2 of 3 |
(In reply to computer solution by Charlie)

If the number contains zeros, but those zeros do not lead either of the halves nor do they merely extend a lower set by a multiple of 100, some non-trivial cases appear with embedded zeros:

24019801       4901       49   99
1587624025 39845    126 155
249001998001 499001    499 999
25027247420176 5002724    1582 2724
48092491265625 6934875    2193 1125
58660847767369 7659037    2422 2787
61009002802276 7810826    2470 1674
81054099030025 9003005    2847 3005

  Posted by Charlie on 2018-12-05 10:56:08
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