Letters

Issue 9
September 1999

Letter from James McGivern

See the letter from James McGivern, an A-Level student, and our Editor's reply in the Staffroom section.


Good wishes

Congratulations for producing one of the most interesting and "user friendly" maths publications I've ever seen !!

Marcelo, Israel

Thanks!


For Your Information

The Goldbach Conjecture (discussed in Issue 2 and Issue 5) has been generalized in the form:

SMARANDACHE CONJECTURE:

Let $k$ >= 3, and 1 <= $s$ < $k$, be integers. Then:

  1. If $k$ is odd, any odd integer can be expressed as a sum of $k-s$ primes (first set) minus a sum of $s$ primes (second set) [such that the primes of the first set are different from the primes of the second set].

    • Is the conjecture true when all $k$ prime numbers are different?

    • In how many ways can each odd integer be expressed as above?

  2. If $k$ is even, any even integer can be expressed as a sum of $k-s$ primes (first set) minus a sum of $s$ primes (second set) [such that the primes of the first set are different from the primes of the second set].

    • Is the conjecture true when all $k$ prime numbers are different?

    • In how many ways can each even integer be expressed as above?

See: http://www.gallup.unm.edu/~smarandache/prim-sum.txt

Dr. M.L.Perez


A suggestion

While searching the web to solve a Fibonacci puzzle, I stumbled upon your web site. I found it quite interesting, and I have bookmarked it to visit later.

I have a suggestion to make. If you do not send an automatic newsletter already, I would like to suggest one. At least a reminder could be sent to the interested readers every month. I am sure many would make it a point to visit the site upon receiving a prompt.

Shankar Mahadevan

Yes, we think this is a good idea too, and we're looking into it!


Who were they?

Who was Pierre Fermat?
What did Isaac Newton do?

Mark and Rob

You can find good biographical material and many useful links at the MacTutor History of Mathematics archive.

Try looking up their entries for Fermat and Newton.


Help!

Hi, I desperately need to know the relationship between perimeter and area when $P = 2n^2 + 10n + 12$ and $A = n^3 + 6n^2 + 11n + 6$.

I cannot factorise the area term as they do not have anything in common. I am 15 and would be greatful for your help.

Pete Mills

If you have factorised the Perimeter term, you must be half way there already. If there is a simple relationship between A and P then it's probably because they have common factors. Why not test each of the factors of the Perimeter expression to see whether they divide the Area expression too?

In general, our student readers should be aware of the askNRICH service at the NRICH site, which is the best place to post queries like these and have them answered by mathematicians and other University students.


How to contact us: Any comments?