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Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

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 ...

An integer j(n) is called a jumping champion if j(n) is the most frequently occurring difference between consecutive primes <=n (Odlyzko et al. 1999). This term was coined by ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...

The nth central trinomial coefficient is defined as the coefficient of x^n in the expansion of (1+x+x^2)^n. It is therefore the middle column of the trinomial triangle, i.e., ...

While the Catalan numbers are the number of p-good paths from (n,n) to (0,0) which do not cross the diagonal line, the super Catalan numbers count the number of lattice paths ...

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).