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Squaring Up The Digits (Posted on 2011-07-28) Difficulty: 2 of 5
Each of X1 and X2 represents a nonzero digit of the 2-digit base M positive integer X1X2; where X1 and X2 are not necessarily distinct.

Determine the possible positive integer values of M, with 2 ≤ M ≤ 101, such that this equation has at least one valid solution.

X12 + X22 = X1X2

Note: X1X2 denotes the concatenation of the two digits.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts observation Comment 2 of 2 |

The non-compliant numbers are those such that n^2+1 is prime; A005574 in Sloane, but I was not able to determine the explanation for this, Ideas, anyone?

  Posted by broll on 2011-07-28 14:14:13
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