Add to ORKGThe representation symbol [a,b,c] is the statement that an integer of n-ic type a is congruent to the sum of an integer of n-ic type b and an integer of n-ic type c. The symbol is extended to include any definite number of elements. New properties, together with a list of symbols involving the n-ic types of specific integers, are derived for use in studying Waring\u27s problem, modulo p, for a particular exponent n. Let Tρ (n) be the least number such that every integer is congruent to the sum of Tρ (n) or fewer n-ic residues. Then for primes of the form 22k + 1, k \u3e 3, 2 ≤ Tρ (11) ≤ 4
. Let p be a prime congruent to \Gamma1 modulo 4, i n p j the Legendre symbol and S(k) = P p\Ga...
AbstractThe ring Zk(+,.) mod pk with prime power modulus (prime p > 2) is analysed. Its cyclic group...
Let E and f be an Eisenstein series and a cusp form, respectively, of the same weight k ≥ 2 and of t...
The representation symbol [a,b,c] is the statement that an integer of n-ic type a is congruent to th...
AbstractThe generalized Jacobi symbol (mn)k is defined for (m, n) = 1, n having prime divisors only ...
AbstractLet A be an ideal in R, the ring of algebraic integers in a number field. The group of resid...
peer reviewedThis article starts a computational study of congruences of modular forms and modular G...
If p be an odd prime, q is said to be an n- ic residue of p if the congruence xn = q (mod p) has sol...
Abstract. Let p be an odd prime and γ(k, pn) be the smallest positive integer s such that every inte...
Includes bibliographical references.After discovering that a pattern existed in the sums of the digi...
An erratum to this article is available at http://dx.doi.org/10.1007/s11537-006-0601-3The congruence...
AbstractThe three sequences mentioned in the title are Ramanujan's τ-function, the coefficients cn o...
AbstractLet p be an odd prime and n an integer relatively prime to p. In this work three criteria wh...
In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is ...
Includes bibliographical references.In this paper a study is first made of the congruence xⁿ ≡ b mod...
. Let p be a prime congruent to \Gamma1 modulo 4, i n p j the Legendre symbol and S(k) = P p\Ga...
AbstractThe ring Zk(+,.) mod pk with prime power modulus (prime p > 2) is analysed. Its cyclic group...
Let E and f be an Eisenstein series and a cusp form, respectively, of the same weight k ≥ 2 and of t...
The representation symbol [a,b,c] is the statement that an integer of n-ic type a is congruent to th...
AbstractThe generalized Jacobi symbol (mn)k is defined for (m, n) = 1, n having prime divisors only ...
AbstractLet A be an ideal in R, the ring of algebraic integers in a number field. The group of resid...
peer reviewedThis article starts a computational study of congruences of modular forms and modular G...
If p be an odd prime, q is said to be an n- ic residue of p if the congruence xn = q (mod p) has sol...
Abstract. Let p be an odd prime and γ(k, pn) be the smallest positive integer s such that every inte...
Includes bibliographical references.After discovering that a pattern existed in the sums of the digi...
An erratum to this article is available at http://dx.doi.org/10.1007/s11537-006-0601-3The congruence...
AbstractThe three sequences mentioned in the title are Ramanujan's τ-function, the coefficients cn o...
AbstractLet p be an odd prime and n an integer relatively prime to p. In this work three criteria wh...
In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is ...
Includes bibliographical references.In this paper a study is first made of the congruence xⁿ ≡ b mod...
. Let p be a prime congruent to \Gamma1 modulo 4, i n p j the Legendre symbol and S(k) = P p\Ga...
AbstractThe ring Zk(+,.) mod pk with prime power modulus (prime p > 2) is analysed. Its cyclic group...
Let E and f be an Eisenstein series and a cusp form, respectively, of the same weight k ≥ 2 and of t...