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 Subtract 1 from squared abbbb (Posted on 2008-08-16)
Determine all possible five digit positive decimal (base 10) integer(s) of the form abbbb, with a ≠ b, that contain no leading zeroes, such that (abbbb2 - 1) is equal to a positive ten digit integer (with no leading zeroes) containing each of the digits 0 to 9 exactly once.

Note: While the solution may be trivial with the aid of a computer program, show how to derive it without one.

 Submitted by K Sengupta Rating: 4.0000 (1 votes) Solution: (Hide) 855552 − 1 = 7319658024, and 977772 − 1 = 9560341728 are the only possible solutions. For an explanation, refer to the solution submitted by Ady TZIDON here, and by Daniel here.

 Subject Author Date re: analytical and brief K Sengupta 2008-08-25 13:05:36 re: Analytical Solution (spoiler) K Sengupta 2008-08-25 13:04:45 Yes, it's trivial with a computer program Charlie 2008-08-17 13:35:13 analytical and brief Ady TZIDON 2008-08-17 10:24:23 Analytical Solution (spoiler) Daniel 2008-08-16 15:29:36 A start (spoiler) Steve Herman 2008-08-16 15:20:25

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