Modulos Math,

is there any rule of thump to solve this
https://www.dropbox.com/s/nrrn50admio9xls/Screenshot%202014-12-30%2011.39.44.jpg?dl=0

Question

Modulos Math,

is there any rule of thump to solve this 
https://www.dropbox.com/s/nrrn50admio9xls/Screenshot%202014-12-30%2011.39.44.jpg?dl=0

ganeshie8 · Answer

reduce both factors in modulo 13

christos · Answer

2611 mod 13
135 mod 13

this?

jhannybean · Answer

How does this work? Can you teach me as well? :P

ganeshie8 · Answer

yes

ganeshie8 · Answer

@Jhannybean basically we want to find the remainder when $2611\times 135$ is divided by $13$

mathmath333 · Answer

$$2611 (\mod 13)\2600+11(\mod 13)\13\times 200+11 (\mod 13)\equiv 11$$

jhannybean · Answer

@mathmath333 can you describe your steps? Haha.

ganeshie8 · Answer

everybody knows this, its just the notation thats new

mathmath333 · Answer

$$135 (\mod 13)\130+5 (\mod 13)\13\times 10+5 \mod 13)\equiv 5$$

mathmath333 · Answer

yes this is very simple

important formula

$(ax+b) (mod ~a)\equiv b$

jhannybean · Answer

Oh, I see.

mathmath333 · Answer

oh very fast u learnt

jhannybean · Answer

Haha no no! I'm still putting it together.

jhannybean · Answer

So the modulus is the divisor.

mathmath333 · Answer

$a$ is the divisor and $b$ is the remainder

ganeshie8 · Answer

yes thats one interpretation

ganeshie8 · Answer

$2611 \mod {13}$ : 

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ganeshie8 · Answer

with mod, you're looking for remainder instead of the quotient

jhannybean · Answer

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