[top-posting corrected]
On Wed, 21 Nov 2007 01:03:03 GMT, Aggie1956
<Jerichey@[EMAIL PROTECTED]
> wrote in
<news:btL0j.22580$lD6.18667@[EMAIL PROTECTED]
> in
alt.algebra.help:
> "Gary S. Simon" <garscosi@[EMAIL PROTECTED]
> wrote in message
> news:garscosi-6AF3A6.13132420112007@[EMAIL PROTECTED]
>> My seven year-old son isn't much for notation. When I
>> asked him the prime factors of 400, he said 2-4-5-2,
>> meaning 2^4 and 5^2.
>> When he asked whether there was any composite number
>> which was the same as its prime factors (using his
>> notation), I told him that I didn't know.
>> Any ideas how to go abouit trying to answer his question?
> Talking to a seven year old (and in this case, a very
> sharp seven year old), I think I would just let him play
> around with the numbers and discover a lot on his own
> while encouraging him even in his failures. For your
> information, the problem he might be having is more in
> the definitions of the terms:
It isn't.
[...]
> The prime factorization of 400 is 2^4 x 5^2 [...]
Which is precisely where Gary's son got his 2-4-5-2.
[...]
> So. Is there any composite number which is the same as its
> prime factors? A composite number would be the product
> of its prime factorization, but the composite would not
> be the same as its prime factors.
All of this is irrelevant and shows that you didn't
understand the question. Here it is in more technical
terms. Suppose that n is a composite number with prime
factorization p_1^{e_1} * p_2^{e_2} * ... * p_k^{e_k}, where
p_1 < p_2 < ... < p_k. Write down a character string s
according to the following algorithm, where '||' denotes
concatenation, and for any positive integer m, d(m) is the
character string representing m in ordinary decimal notation
without leading zeroes:
set s to the null string
for i = 1 to k
let s = s||d(p_i)
if e_i > 1 then let s = s||d(e_i)
end for
The question is whether there is any composite n for which
s = d(n).
Brian
|
