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Implementation rest modulo 2 needed


Dear Mathematica Gurus,

I want to construct algorhitm finding two divisors of numbers (without 
FactorIneteger and with uses only Reduce, GroebnerBasis etc.)

e.g. for divisors of number 15 in binary system these will be

Reduce[{x a == 1 && y a + x b == 1 && y b + x c == 1 && y c == 1 &&
  x (x - 1) == 0 && y (y - 1) == 0 && c (c - 1) == 0 &&
  b (b - 1) == 0 && a (a - 1) == 0}, {x, y, a, b, c}, Integers]

but to find divisors of 15=1111 wasn't necessary to use rest modulo 2

How do that for e.g. 735 = 1011011111 where we have to uses rest modulo 2

Any idea ?

Best wishes
Artur



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