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A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

A palindromic prime is a number that is simultaneously palindromic and prime. The first few (base-10) palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, ...

The negative real axis is the portion of the real axis with x<0.

The positive real axis is the portion of the real axis with x>0.

A Goldbach number is a positive integer that is the sum of two odd primes (Li 1999). Let E(x) (the "exceptional set of Goldbach numbers") denote the number of even numbers ...

A superabundant number is a composite number n such that sigma(n)/n>sigma(k)/k for all k<n, where sigma(n) is the divisor function. Superabundant numbers are closely related ...

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...

Consider an n-digit number k. Square it and add the right n digits to the left n or n-1 digits. If the resultant sum is k, then k is called a Kaprekar number. For example, 9 ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...