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The operating of shifting the leading digits of an addition into the next column to the left when the sum of that column exceeds a single digit (i.e., 9 in base 10).

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

A sum of the elements from some set with constant coefficients placed in front of each. For example, a linear combination of the vectors x, y, and z is given by ax+by+cz, ...

The nth cubic number n^3 is a sum of n consecutive odd numbers, for example 1^3 = 1 (1) 2^3 = 3+5 (2) 3^3 = 7+9+11 (3) 4^3 = 13+15+17+19, (4) etc. This identity follows from ...

The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.

Diagonalize a form over the rationals to diag[p^a·A,p^b·B,...], where all the entries are integers and A, B, ... are relatively prime to p. Then Sylvester's signature is the ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

The "Foxtrot series" is a mathematical sum that appeared in the June 2, 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007). It arose from a ...