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Let T(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Define f_m(x)=product_(t in T(m))(x-t). (1) Then a ...

Let m>=3 be an integer and let f(x)=sum_(k=0)^na_kx^(n-k) be an integer polynomial that has at least one real root. Then f(x) has infinitely many prime divisors that are not ...

The Baum-Sweet sequence is the sequence of numbers {b_n} such that b_n=1 if the binary representation of n contains no block of consecutive 0s of odd length, and b_n=0 ...

11 21 3 41 4 7 81 5 11 15 161 6 16 26 31 32 (1) The number triangle illustrated above (OEIS A008949) composed of the partial sums of binomial coefficients, a_(nk) = ...

Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

A divisor d of a positive integer n is biunitary if the greatest common unitary divisor of d and n/d is 1. For a prime power p^y, the biunitary divisors are the powers 1, p, ...

The third-order ordinary differential equation 2y^(''')+yy^('')=0. This equation arises in the theory of fluid boundary layers, and must be solved numerically (Rosenhead ...

The order-n bouquet graph B_n is a pseudograph consisting of a single vertex with n self-loops. The bouquet graph B_1 is a pseudograph that can be considered to correspond to ...

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

In 1850, Bravais demonstrated that crystals were comprised of 14 different types of unit cells: simple cubic, body-centered cubic, face-centered cubic; simple tetragonal, ...