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Consider solutions to the equation x^y=y^x. (1) Real solutions are given by x=y for x,y>0, together with the solution of (lny)/y=(lnx)/x, (2) which is given by ...

A prime-distance graph is a distance graph with distance set given by the set of prime numbers.

The prime signature of a positive integer n is a sorted list of nonzero exponents a_i in the prime factorization n=p_1^(a_1)p_2^(a_2).... By definition, the prime signature ...

A principal ideal domain is an integral domain in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

The pseudosmarandache function Z(n) is the smallest integer such that sum_(k=1)^(Z(n))k=1/2Z(n)[Z(n)+1] is divisible by n. The values for n=1, 2, ... are 1, 3, 2, 7, 4, 3, 6, ...

Quinn et al. (2007) investigated a class of N coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of sinphi∼1-c_1/N, with an experimental ...

The algorithm of constructing and interpreting a quotient-difference table which allows interconversion of continued fractions, power series, and rational functions ...

Given the generating functions defined by (1+53x+9x^2)/(1-82x-82x^2+x^3) = sum_(n=1)^(infty)a_nx^n (1) (2-26x-12x^2)/(1-82x-82x^2+x^3) = sum_(n=0)^(infty)b_nx^n (2) ...

A random variate is a variable generated from uniformly distributed pseudorandom numbers. Depending on how they are generated, a random variate can be uniformly or ...