Continued fraction expansions of rational expressions with irreducible denominators in characteristic 2

AbstractGiven any irreducible polynomial q of degree n over the field with two elements, there is a sequence of polynomials pn, pn…1,…, p0 with pn = q, with p0 = 1, with the degree of pi equal to i, and with pi ≡ pi…2 (mod pi−1). In other words, given an irreducible q there is a p, relatively prime to q, with degree one less and such that the degrees of the remainders in Euclid's Algorithm for the greatest common divisor of p and q go down by exactly 1 at each step

Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers

We give new lower bounds for the Schur numbers S(6) and S(7). This will imply new lower bounds for the Multicolor Ramsey Numbers R6(3) and R7(3). We also make several observations concerning symmetric sumfree partitions into 5 sets