Question

FAN AND MEDAL!

Which is a counterexample to the conjecture?

Any number that is divisible by 3 is divisible by 9.

Answer 1

6

Answer 2

think of a number less than 9 which is divisible by 3

Answer 3

12 is another counterexample

Answer 4

It doesn't have to be less than 9, it just can't be a multiple of 9 :)

Answer 5

so what is right?

Answer 6

6 or 12??

Answer 7

both

Answer 8

i didnt say it had to be less than 9 - i was just giving a hint

Answer 9

any number with the prime factorization will work
\[3 \cdot 2^k \cdot 5^k \cdot 7^k \cdot 11^{k}\cdot 13^k \cdot 17^k \cdots p^k \cdots \]
where p is a prime number not equal to 3
and k is a non-negative integer

Answer 10

well and all those k's could be different :p

Answer 11

\[3 \cdot 2^{k_1} \cdot 5^{k_2} \cdot 7^{k_3} \cdot 11^{{k_4}}\cdot 13^{k_5} \cdot 17^{k_6} \cdots p^{k_n} \cdots\]
where the k_i values are non-negative