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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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Solution Answer Comment 4 of 4 |
7^2=49
97^2=9409
997^2=994009
9997^2=99940009
99997^2=9999400009
...
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997^2=9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
Therefore, a=4.


  Posted by Math Man on 2020-11-15 18:53:05
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