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Let X_1 and X_2 be the number of successes in variates taken from two populations. Define p^^_1 = (x_1)/(n_1) (1) p^^_2 = (x_2)/(n_2). (2) The estimator of the difference is ...

The present value v_n of a single payment made at n periods in the future is v_n=p/((1+r)^n), (1) where n is the number of periods until payment, p is the payment amount, and ...

The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

Let there be x successes out of n Bernoulli trials. The sample proportion is the fraction of samples which were successes, so p^^=x/n. (1) For large n, p^^ has an ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...

Let the difference of successive primes be defined by d_n=p_(n+1)-p_n, and d_n^k by d_n^k={d_n for k=1; |d_(n+1)^(k-1)-d_n^(k-1)| for k>1. (1) N. L. Gilbreath claimed that ...

17 is a Fermat prime, which means that the 17-sided regular polygon (the heptadecagon) is constructible using compass and straightedge (as proved by Gauss).

To enumerate a set of objects satisfying some set of properties means to explicitly produce a listing of all such objects. The problem of determining or counting all such ...

A finite, increasing sequence of integers {n_1,...,n_m} such that sum_(i=1)^m1/(n_i)-product_(i=1)^m1/(n_i) in N. A sequence is a Giuga sequence iff it satisfies ...

If m is an integer, then for every residue class r (mod m), there are infinitely many nonnegative integers n for which P(n)=r (mod m), where P(n) is the partition function P.