Hi all.

I'm trying to figure out the following problem:

Find the number of positive integers not exceeding 1000 that are divisible by 3 but not by 4.

Help will be appreciated. Looking for a simple/elementary proof.

Thanks.

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- May 21st 2010, 06:51 AMpollardrho06Divisibility
Hi all.

I'm trying to figure out the following problem:

Find the number of positive integers not exceeding 1000 that are divisible by 3 but not by 4.

Help will be appreciated. Looking for a simple/elementary proof.

Thanks. - May 21st 2010, 06:58 AMFailure
- May 21st 2010, 10:47 AMpollardrho06
- May 21st 2010, 11:36 AMwonderboy1953Hint
Look for cycles.

- May 21st 2010, 02:22 PMSoroban
Hello, pollardrho06!

Quote:

Find the number of positive integers not exceeding 1000

that are divisible by 3 butby 4.*not*

Every third number is divisible by 3.

. . There are: . numbers divisible by 3.

But every twelfth number is divisible by 3by 4.*and*

. . There are: . multiples of 3 whichdivisible by 4.*are*

Therefore, there are: . such numbers.

- May 21st 2010, 02:46 PMpollardrho06