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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 ...

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 ...

By way of analogy with the eban numbers, aban numbers are defined as numbers whose English names do not contain the letter "a" (i.e., "a" is banned). Note that this ...

Relations in the definition of a Steenrod algebra which state that, for i<2j, Sq^i degreesSq^j(x)=sum_(k=0)^(|_i/2_|)(j-k-1; i-2k)Sq^(i+j-k) degreesSq^k(x), where f degreesg ...

Given an acute angle in a right triangle, the adjacent side is the leg of the triangle from which the angle to the hypotenuse is measured. Lengths of adjacent and opposite ...

The term "aliquot divisor" is commonly used to mean two distinct but related things. The first definition is a number that divides another exactly. For instance, 1, 2, 3, and ...

An expression is said to be ambiguous (or poorly defined) if its definition does not assign it a unique interpretation or value. An expression which is not ambiguous is said ...

The sequence whose definition is: "t is the first, fourth, eleventh, ... letter of this sentence." The first few values are 1, 4, 11, 16, 24, 29, 33, 35, 39, ... (OEIS ...