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Posted
This is very useful. Can you explain why 8765^4321 mod 9 = 8^4321 mod 9?

Although I know 8765 mod 9 = 8.

 

It's just the basic rules of modular arithmetic. Google "modular arithmetic".

Remember' date=' I'm using the "=" sign instead of the congruence sign. It's just quicker to type =.

 

Similarily, why 8^2160 mod 9 = 8?

I didn't say that. I said:

8^2 = 64 = 1 mod 9

Therefore,

(8^2)^2160 = (1)^2160 mod 9

Posted

I got it now, thank you. actually 8 mod 9=-1,

Posted

It's not something you'll find outside university level (normally). I've only just started it properly at the end of last year (in the 1st year of my maths degree), and that was nothing but a cursory glance. If you do a degree that involves quite a lot of maths (Physics, Computer Science, etc) you'll get a maths course in the first year that will probably have some kind of introduction to modular arithmetic.

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