a, b, and x are positive integers such that
sqrt(a) + sqrt(b) = sqrt(x)
How many possible values of x less than or equal to 1000 are there?
(In reply to
re: Independent Solution by John Reid)
You are correct about my counting method. I was methodically
counting the numbers below 1000 that had no more than 1 of each prime
in the prime factorization. I'm glad you spotted my error.
I knew when I saw that yours differed by 1 that I probably made a
counting error. When I did so much counting by hand, I was bound
to make an error somewhere.
I have since read your solution. I think it's amazing how we came
to the same conclusions and counted the same number with completely
different methods! I didn't think of using combinatorics for the
counting method. I love combinatorics, and I kept on wondering if
I could use it to avoid all that tedious counting.
I think the other solutions do not agree because of a misinterpretation
of the problem. When I started reading the comments, it seemed
everyone was trying to count the number of possible sums rather than
the number of possible values of x. I lost interest, and wrote my
own solution instead. I think I mentioned in my solution that
counting the number of sums was a lot more difficult.
|
|
Posted by Tristan
on 2005-05-06 05:53:45 |
re(2): Independent Solution
