perplexus.info :: Numbers : Fit the middle digit

Fit the middle digit (Posted on 2020-11-12)

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: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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