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modulo a prime p, there is an analogous theory to the classical theory of complex modular forms and the p-adic theory of modular forms. Modular forms...

if a is coprime with m. This integer a−1 is called a modular multiplicative inverse of a modulo m. If a ≡ b (mod m) and a−1 exists, then a−1 ≡ b−1 (mod...

Modulo (disambiguation) – many uses of the word modulo, all of which grew out of Carl F. Gauss's introduction of modular arithmetic in 1801. Modulo (mathematics)...

calculation of modular multiplicative inverses. For a given positive integer m, two integers, a and b, are said to be congruent modulo m if m divides...

cyclic shifts". Look up modulo in Wiktionary, the free dictionary. Essentially unique List of mathematical jargon Up to "Modular arithmetic". Encyclopedia...

division and reduction modulo R are inexpensive, and the modulus is not useful for modular multiplication unless R > N. The Montgomery form of the residue class...

In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive...

remainder of c = 8. Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the...

work can be interpreted as implicitly using p-adic numbers. Roughly speaking, modular arithmetic modulo a positive integer n consists of "approximating"...

modular group has a trivial center, and thus the modular group is isomorphic to the quotient group of B3 modulo its center; equivalently, to the group of inner...

In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of...

of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements...

rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic...

a quadratic nonresidue modulo n. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues...

states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In the notation of modular arithmetic, this...

with equivalence classes more effective. For example, in modular arithmetic, the canonical form for a residue class is usually taken as the least non-negative...

fundamental objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence subgroups in more...

fundamental domain of Γ {\displaystyle \Gamma } . In contrast to modular forms, Maass forms need not be holomorphic. They were studied first by Hans Maass...

integer n, the set of integers modulo n, again with the operation of addition, forms a finite cyclic group, denoted Z/nZ. A modular integer i is a generator...

preceding the factor, p − 1, is powersmooth; the essential observation is that, by working in the multiplicative group modulo a composite number N, we...