Devise an algorithm which, for any polynomial P(x), will determine the polynomial remainder of P(x)/(x^2+x+1) without actually performing the division.

This is quite an interesting exercise. 

While I don't have time to go into it at the moment the process can be achieved by 'manipulating' the coefficients of the 'x' powers.

This is done by adding together certain values whilst subtracting others. 

The remainder will have two numerical values, one is the coefficient of any residual x^1 and the other xº.

I shall post more fully a little later unless someone presents something along my thoughts.

Posted by brianjn on 2008-04-16 11:23:11