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# Interesting property with 9

I want to get clarified with numbers ending with 9. I have considered 2 digit numbers and not extending it further as of now.

If we have 2 digit numbers of the form 10a + b and ending with 9,


Then, $$ab + a+b= 10a+b$$.

Note by Ashwin K
1 year, 1 month ago

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I assume that $$a$$ is a single digit positive integer and $$b$$ is a non-negative single digit integer, then obviously $$b=9$$ and so your equation holds true. · 1 year, 1 month ago

Yes..I considered only 2 digit numbers. I need to know how it works! · 1 year, 1 month ago

After you know that $$b=9$$, what happens when you substitute $$b=9$$ into the equation $$ab + a +b = 10a + b$$? · 1 year, 1 month ago

consider any single digit value for a,

For instance a =1, the equation becomes 1*9 + 1 + 9 = 19 = 10(1) + 9 = 19. · 1 year, 1 month ago

You can do that as well for $$a=2,3,\ldots,9$$, but that is tiresome.

I asked you to substitute $$b=9$$ alone only, nothing else. What happens to the equation $$ab+ab+b=10a+b$$ after you substitute $$b=9$$? · 1 year, 1 month ago

Got you. both side equations are becoming equal. Can we extend this for 3 digit numbers. Do u have any idea? · 1 year, 1 month ago

Hmmm, yes we can, by assuming your last digit is already given, then you can make up any equation as you like. But I doubt any of these identity are useful, because it is too specific and are not applicable in the first place. · 1 year, 1 month ago

9 always been a magic number. Knowing it's property will always be handy. I made up this note after solving a problem of this kind. · 1 year, 1 month ago

No, it's not. What is so special about 9? · 1 year, 1 month ago

It is magical number because we consider base 10 in our number system and thus last number '9' has to be Special. In general, last digit in that number system will carry special properties. · 1 year, 1 month ago

That made no sense, I could call the number 8 special because "the second last number '8' has to be special". · 1 year, 1 month ago

There are interesting properties on it buddy. This is not my judgement. I think I am not convincing you. Just Google it for yourselves and check. · 1 year, 1 month ago

The number 8 also has interesting properties. · 1 year, 1 month ago

Wow..let me know that. · 1 year, 1 month ago

Read up application of divisibility rules. · 1 year, 1 month ago