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Useful in cryptarithmetic

76^2 always end with 76 (e.g. 176^ = 30976)

376^2 always end with 376 (e.g. 376^2 = 141376 and 1376^2 = 1893376)

9376^2 end with 9376

25^2 always end with 625 (e.g. 125^2 = 15625 or 325^2 = 105625)

625^2 always end with 625 (e.g. 1625^2 = 2640625 or 2625^2 = 6890625)

24^even number always end with 76 and 24^odd No. always end with 24

The number having xxx90625^2 ends with 90625

Note by Sunil Pradhan
2 years, 10 months ago

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It was just an observation.

Sunil Pradhan - 2 years, 10 months ago

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That's an interesting pattern. Do you know how to generalize it?
Is there always some \(n-\) digit number \(A\) such that \(A^2\) ends with \(A\)?
Are there any other sequences, or do we only have these 2? For example, could we have a number that ended with 01?

Why, or why not?

Calvin Lin Staff - 2 years, 10 months ago

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