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A Keith number is an n-digit integer N>9 such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed with the ...

The de Longchamps ellipse of a triangle DeltaABC is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt X_(57). (Since a ...

The triangle of numbers A_(n,k) given by A_(n,1)=A_(n,n)=1 (1) and the recurrence relation A_(n+1,k)=kA_(n,k)+(n+2-k)A_(n,k-1) (2) for k in [2,n], where A_(n,k) are shifted ...

Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

The chi distribution with n degrees of freedom is the distribution followed by the square root of a chi-squared random variable. For n=1, the chi distribution is a ...

Let p(d,a) be the smallest prime in the arithmetic progression {a+kd} for k an integer >0. Let p(d)=maxp(d,a) such that 1<=a<d and (a,d)=1. Then there exists a d_0>=2 and an ...

Consider the decimal expansion of the reciprocal of the number seven, 1/7=0.142857142857...=0.142857^_, (1) which is a repeating decimal. Now take overlapping pairs of these ...

The system of partial differential equations u_t = b·v_x (1) b_(xt) = u_(xx)b+axv_x-2vx(vxb). (2)

Let P=alpha_1:beta_1:gamma_1 and Q=alpha_2:beta_2:gamma_2 be points, neither of which lie on a sideline of the reference triangle DeltaABC. The P-Ceva conjugate X of Q is ...

Schroeder (1991) calls the ceiling function symbols [ and ] the "gallows" because of their similarity in appearance to the structure used for hangings.