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A Carmichael number is an odd composite number n which satisfies Fermat's little theorem a^(n-1)-1=0 (mod n) (1) for every choice of a satisfying (a,n)=1 (i.e., a and n are ...

omega^epsilon=epsilon, where omega is an ordinal number and epsilon is an inaccessible cardinal.

Any prime number other than 2 (which is the unique even prime). Humorously, 2 is therefore the "oddest" prime.

The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

The term energy has an important physical meaning in physics and is an extremely useful concept. There are several forms energy defined in mathematics. In measure theory, let ...

A (2n)×(2n) complex matrix A in C^(2n×2n) is said to be Hamiltonian if J_nA=(J_nA)^(H), (1) where J_n in R^(2n×2n) is the matrix of the form J_n=[0 I_n; I_n 0], (2) I_n is ...

A real-valued univariate function f=f(x) has a jump discontinuity at a point x_0 in its domain provided that lim_(x->x_0-)f(x)=L_1<infty (1) and lim_(x->x_0+)f(x)=L_2<infty ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...