Hi! Can anybody pls prove the rules of divisibility for 4, 5,6,9, & 11 using modular arithmetic if possible.

I don't really get the proofs I searched from the net. Thanks! :D

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- Jan 23rd 2010, 11:42 PMcookiejarProofs of rules of divisibility
Hi! Can anybody pls prove the rules of divisibility for 4, 5,6,9, & 11 using modular arithmetic if possible.

I don't really get the proofs I searched from the net. Thanks! :D - Jan 24th 2010, 06:59 AMDinkydoeQuote:

Hi! Can anybody pls prove the rules of divisibility for 4, 5,6,9, & 11

- Jan 24th 2010, 10:47 AMMoo
Proofs of divisibility, do you mean :

- 4 : last two digits form a number which is a multiple of 4

- 5 : ends by 0 or 5

- 6 : multiple by 2 & 3

- 9 : sum of digits makes a multiple of 9

- 11 : difference of alternate sums is a multiple of 11

?

If so, what specifically don't you understand ?

For 4, write the number as 100k+..

For 5, write the number as 10k+.

For 6, chinese remainder theorem

For 9, write the number as a linear combination of powers of 10, and while working modulo 9, it should be obvious

For 11, same thing as 9