perplexus.info :: Numbers : Off by one

Off by one (Posted on 2013-01-18)

N=(abcabd) is a 6-digit number with d-c=1.

FIND N, given it is an even square.

Rem: (abcabd) denotes chaining (= concatenation), not a product

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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solving mod 1001

Comment 7 of 7 |

N^2 = abcabd = abcabc + 1 = abc(1001) + 1 gives N^2 = 1 mod1001 with solutions +-1, +-155, +-274, +-428.

N = +-1, 155, 274 gives solutions that are beyond the problem's range but -155 + 1001 = 846, -274 + 1001 = 727, 428, and -428 + 1001 = 573 gives valid solutions.

Posted by xdog on 2013-01-19 15:53:15

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