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An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

The Borwein integrals are the class of definite integrals defined by I_n=1/piint_0^inftyx^(-(n+1)/2)product_(k=1,3,...)^nsin(x/k)dx for odd n. The integrals are curious ...

A Colbert number is any prime number with more than 1000000 decimal digits whose discovery contributes to the long-sought after proof that k=78557 is the smallest Sierpiński ...

A set function mu possesses countable additivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

The partial order width of a set P is equal to the minimum number of chains needed to cover P. Equivalently, if a set P of ab+1 elements is partially ordered, then P contains ...

A pair of prime numbers (p,q) such that p^(q-1)=1 (mod q^2) and q^(p-1)=1 (mod p^2). The only known examples are (2, 1093), (3, 1006003), (5 , 1645333507), (83, 4871), (911, ...

Given the Lucas sequence U_n(b,-1) and V_n(b,-1), define Delta=b^2+4. Then an extra strong Lucas pseudoprime to the base b is a composite number n=2^rs+(Delta/n), where s is ...

Gram's law (Hutchinson 1925; Edwards 2001, pp. 125, 127, and 171) is the tendency for zeros of the Riemann-Siegel function Z(t) to alternate with Gram points. Stated more ...

The half-altitude triangle DeltaA^'B^'C^' of a reference triangle DeltaABC is defined by letting A^' be the midpoint between vertex A and the foot of the A-altitude on side ...