Interesting question

[Neil Fernandez]

In message <48A9808F.4080303 at gambitcomm.com>, David Wilson
<dwilson at gambitcomm.com> writes

>What positive integers are of the form wx+xy+yz+zw where w,x,y,z are 
>positive integers?

Less than 100, only the composites.

Neil

-- 
Neil Fernandez



>I don't know if there's a theorem to that effect. I do know that there
>are polynomials in several variables whose positive values are the
>primes (but I'm not sure what the conditions are on the variable
>values). I don't know if there is a known nontrivial lower limit on the
>number of necessary variables to achieve this.
>
>Anyway, here we are talking about numbers NOT of the specified form,
>which I think is a whole nother beastie (people actually say "a whole
>nother" in preference to "a whole other"). At any rate, the observation
>that xy+yz+zw+wx = (x+y)(z+w) makes it obvious that the expression takes
>on composite values when x,y,z,w are positive integers. What's
>interesting is that x1*x2 + x2*x3 + ... + x_n*x1 seems to be factorable
>like this only for n = 4.

Here's the sequence for 5 terms: A101902.

Tony