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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

Think of any number that is a multiple of five.

Eg. - **65**.

65 is between **6**0 and **7**0. So multiply them in your mind **6**0×**7**0=**42**00. Attach 25 in the end.**∴65²= 4225.**

Can you guess why it works?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,727

Hi 123ronnie321;

If a is the number you want to square and it ends in 5 then adding 5 and subtracting 5 will produce ( a + 5 ) ( a - 5).

So a^2 = ( a + 5 ) ( a - 5).= a^2 - 25

The only way to make this equation true is to add 25 to the RHS,

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

Hi Bobbym,

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,727

Hi;

How are you doing with the Vilenkin book?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

I read the first few pages and found it interesting. The author has given some nice practical examples about where this field is used.

I have no idea about computers but he has given some nice information on "small" computer 'Strela'.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,727

Hi 123ronnie321;

Good! Combinatorics is a fun part of math. It is growing rapidly into one of the most important parts of math.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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