Let . Then . Notice that so and . That is, iff

If you aren't familiar with congruences, notice that:

For divisibility by 3, notice that and argue in the same way as in the case with divisibility by 9.

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- Sep 6th 2009, 02:07 AM #1

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## numbertheory

hi can anyone help me with this problem in number theory with regards to prime number? i don't know how to proive this..can someone help?

Prove that an integer is divisible by 3 if and only if the sum of its digits is divbisble by 3. Prove that an integer is divisible by 9 if and only if the sum of its digits is divisible by 9...thanls

- Sep 6th 2009, 02:41 AM #2

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Let . Then . Notice that so and . That is, iff

If you aren't familiar with congruences, notice that:

For divisibility by 3, notice that and argue in the same way as in the case with divisibility by 9.

- Sep 6th 2009, 03:08 AM #3

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