Interesting question

David Wilson dwilson at
Mon Aug 18 18:02:01 CEST 2008

Yes, that neatly solves the problem.

I started out looking at what numbers were not of the form xy+yz+zx for 
positive integers, which turns out to be a hard problem (it's A025052 + 
possibly one other very large term). Naturally, I went on to check 
numbers not of the from wx+xy+yz+zw, and was surprised to see the 1 and 
the primes. The factorization makes the solution trivial. The 
interesting thing, i guess, is that a factorization exists only for a 
4-term expression of this sort.

So on to five terms.

Azarian, Mohammad K. wrote:
> Is it helpful to say that which integers are of the form mn=(x+z)(w+y)?

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