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Fit the middle digit (Posted on 2020-11-12) Difficulty: 3 of 5
Determine all possible digits a for which 9...9a0...09 is a square number. (Excluding the digit a there are 101 9's and 100 0's in the number)

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

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Some Thoughts One small observation | Comment 3 of 4 |
Squares, mod 9, are either 0, 1, 4 or 7.
The given number mod 9 equals a.
So, if the number is square, then a equals 0, 1, 4 or 7.

This is a necessary but not sufficient condition.

  Posted by Steve Herman on 2020-11-12 20:41:07
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