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

#NumberTheory

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

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 - 6 years, 5 months ago

It was just an observation.

Sunil Pradhan - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$