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Let A and B be any sets, and let |X| be the cardinal number of a set X. Then cardinal exponentiation is defined by |A|^(|B|)=|set of all functions from B into A| (Ciesielski ...

A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors (excluding 1). (The primes are excluded since they trivially ...

If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

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 ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

Let A and B be any sets with empty intersection, and let |X| denote the cardinal number of a set X. Then |A|+|B|=|A union B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; ...

A Stoneham number is a number alpha_(b,c) of the form alpha_(b,c)=sum_(k=1)^infty1/(b^(c^k)c^k), where b,c>1 are relatively prime positive integers. Stoneham (1973) proved ...

The values of -d for which imaginary quadratic fields Q(sqrt(-d)) are uniquely factorable into factors of the form a+bsqrt(-d). Here, a and b are half-integers, except for ...

A round number is a number that is the product of a considerable number of comparatively small factors (Hardy 1999, p. 48). Round numbers are very rare. As Hardy (1999, p. ...

The conjecture due to Pollock (1850) that every number is the sum of at most five tetrahedral numbers (Dickson 2005, p. 23; incorrectly described as "pyramidal numbers" and ...