An extension of the Lucas theorem
An extension of the theorem of Bauer and polynomials of certain special types
An ideal Waring problem with restricted summands
An idelic approach to the wild kernel.
An identity for a class of arithmetical functions of several variables.
An identity for a class of arithmetical functions of two variables.
An identity for sums of polylogarithm functions.
An identity generator: basic commutators.
An identity involving Dedekind sums and generalized Kloosterman sums
The various properties of classical Dedekind sums have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of...
An identity involving multiplicative orders.
An identity involving Ramanujan's sum.
An identity Ramanujan probably missed
"Ramanujan's 6-10-8 identity" inspired Hirschhorn to formulate his "3-7-5 identity". Now, we give a new "6-14-10 identity" which we suppose Ramanujan would have discovered but missed to mention in his notebooks.
An implementation of the number field sieve.
An improved algorithm for the solution of integer programs by the solution of associated diophantine equations
An Improved Bound for Prime Solutions of Some Ternary Equations.
An improved estimate concerning 3n+1 predecessor sets
An improved estimate on the distribution mod 1 of powers of real matrices
An improved result on irregularities in distribution of sequences of integers
In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
An improved upper bound for G(k) in Waring's problem for relatively small k
An improved upper bound for the discrepancy of quadratic congruential pseudorandom numbers