perplexus.info :: Just Math : Subtract 1 from squared abbbb

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.

Comments: ( You must be logged in to post comments.)

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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