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The w-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. Setting f_n(1)=f_n (1) give a Fermat-Lucas number. The first few Fermat-Lucas ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

Given the Lucas sequence U_n(b,-1) and V_n(b,-1), define Delta=b^2+4. Then an extra strong Lucas pseudoprime to the base b is a composite number n=2^rs+(Delta/n), where s is ...

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...

Let P, Q be integers satisfying D=P^2-4Q>0. (1) Then roots of x^2-Px+Q=0 (2) are a = 1/2(P+sqrt(D)) (3) b = 1/2(P-sqrt(D)), (4) so a+b = P (5) ab = 1/4(P^2-D) (6) = Q (7) a-b ...

The Lucas central triangle (a term coined here for the first time) is the triangle DeltaL_AL_BL_C formed by the centers of the Lucas circles of a given reference triangle ...

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

The points of tangency of the Lucas inner circle with the Lucas circles are the inverses of the vertices A, B, and C in the Lucas circles radical circle. These form the Lucas ...

The Lucas cubic is a pivotal isotomic cubic having pivot point at Kimberling center X_(69), the isogonal conjugate of the orthocenter, i.e., the locus of points P such that ...