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If there exists a rational integer x such that, when n, p, and q are positive integers, x^n=q (mod p), then q is the n-adic residue of p, i.e., q is an n-adic residue of p ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

In the most commonly used convention (e.g., Apostol 1967, pp. 205-207), the second fundamental theorem of calculus, also termed "the fundamental theorem, part II" (e.g., ...

Church proved several important theorems that now go by the name Church's theorem. One of Church's theorems states that there is no consistent decidable extension of Peano ...

Let the multiples m, 2m, ..., [(p-1)/2]m of an integer such that pm be taken. If there are an even number r of least positive residues mod p of these numbers >p/2, then m is ...

A statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule (duality principle), or ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

When a measure lambda is absolutely continuous with respect to a positive measure mu, then it can be written as lambda(E)=int_Efdmu. By analogy with the first fundamental ...

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

There are at least two theorems known as Chebyshev's theorem. The first is Bertrand's postulate, proposed by Bertrand in 1845 and proved by Chebyshev using elementary methods ...