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| Subtract 1, get a square (Posted on 2009-06-24) |
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By subtracting 1 from the positive base N integer having the form XYXYXYZY, we get a perfect square. It is known that each of X, Y and Z represents a different base N digit from 0 to N-1, and X is nonzero.
What are the integer value(s) of N, with 3 ≤ N ≤ 16 for which this is possible?
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Submitted by K Sengupta
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Rating: 5.0000 (1 votes)
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Solution:
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(Hide)
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This is possible for all integer values of N except 4 in the range 3 to 16 inclusively.
For an explanation refer to the solution submitted by Daniel in this location.
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In this location, Daniel has provided a general proof whereby (X, Y, Z) = (N-2, 2, 0) will always be a solution in base N, whenever N is any positive integer ≥ 3, but N ≠ 4.
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