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A Størmer number is a positive integer n for which the greatest prime factor p of n^2+1 is at least 2n. Every Gregory number t_x can be expressed uniquely as a sum of t_ns ...

A superior highly composite number is a positive integer n for which there is an e>0 such that (d(n))/(n^e)>=(d(k))/(k^e) for all k>1, where the function d(n) counts the ...

By analogy with the tanc function, define the tanhc function by tanhc(z)={(tanhz)/z for z!=0; 1 for z=0. (1) It has derivative (dtanhc(z))/(dz)=(sech^2z)/z-(tanhz)/(z^2). (2) ...

The tetranacci numbers are a generalization of the Fibonacci numbers defined by T_0=0, T_1=1, T_2=1, T_3=2, and the recurrence relation T_n=T_(n-1)+T_(n-2)+T_(n-3)+T_(n-4) ...

Every closed three-manifold with finite fundamental group has a metric of constant positive scalar curvature, and hence is homeomorphic to a quotient S^3/Gamma, where Gamma ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

Two submanifolds X and Y in an ambient space M intersect transversally if, for all p in X intersection Y, TX_p+TY_p={v+w:v in TX_p,w in TY_p}=TM_p, where the addition is in ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

Following Yates (1980), a prime p such that 1/p is a repeating decimal with decimal period shared with no other prime is called a unique prime. For example, 3, 11, 37, and ...