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Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

A square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

The number k in the expression s(n)=kn for a multiperfect number is called its class.

A conjecture due to Paul Erdős and E. G. Straus that the Diophantine equation 4/n=1/a+1/b+1/c involving Egyptian fractions always can be solved (Obláth 1950, Rosati 1954, ...

Bourque and Ligh (1992) conjectured that the least common multiple matrix on a GCD-closed set S is nonsingular. This conjecture was shown to be false by Haukkanen et al. ...

A number n is called wasteful if the number of digits in the prime factorization of n (including powers) uses more digits than the number of digits in n. The first few ...

A number n for which a shortest chain exists which is a Brauer chain is called a Brauer number. There are infinitely many non-Brauer numbers.

Euler (1772ab) conjectured that there are no positive integer solutions to the quartic Diophantine equation A^4=B^4+C^4+D^4. This conjecture was disproved by Elkies (1988), ...

The number (10^(666))!, where 666 is the beast number and n! denotes a factorial. The number has approximately 6.656×10^(668) decimal digits. The number of trailing zeros in ...