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If the integral coefficients C_0, C_1, ..., C_(N-1) of the polynomial f(x)=C_0+C_1x+C_2x^2+...+C_(N-1)x^(N-1)+x^N are divisible by a prime number p, while the free term C_0 ...

The improvement of the convergence properties of a series, also called convergence acceleration or accelerated convergence, such that a series reaches its limit to within ...

A method for finding recurrence relations for hypergeometric polynomials directly from the series expansions of the polynomials. The method is effective and easily ...

Let U(P,Q) and V(P,Q) be Lucas sequences generated by P and Q, and define D=P^2-4Q. (1) Then {U_((n-(D/n))/2)=0 (mod n) when (Q/n)=1; V_((n-(D/n))/2)=D (mod n) when (Q/n)=-1, ...

Let p be prime and r = r_mp^m+...+r_1p+r_0 (0<=r_i<p) (1) k = k_mp^m+...+k_1p+k_0 (0<=k_i<p), (2) then (r; k)=product_(i=0)^m(r_i; k_i) (mod p). (3) This is proved in Fine ...

Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

A link L is said to be splittable if a plane can be embedded in R^3 such that the plane separates one or more components of L from other components of L and the plane is ...

The arf invariant is a link invariant that always has the value 0 or 1. A knot has Arf invariant 0 if the knot is "pass equivalent" to the unknot and 1 if it is pass ...

The cyclotomic graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a cube in the finite field GF(q). This graph is ...

The Diffie-Hellman protocol is a method for two computer users to generate a shared private key with which they can then exchange information across an insecure channel. Let ...