On the powers of Motzkin paths.
On the power-series expansion of a rational function
Introduction. The problem of determining the formula for , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of[(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part of the solution...
On the p-rank of the tame kernel of algebraic number fields.
On the prime density of Lucas sequences
The density of primes dividing at least one term of the Lucas sequence , defined by and for , with an arbitrary integer, is determined.
On the prime factors of non-congruent numbers
We give infinitely many new families of non-congruent numbers where the first prime factor of each number is of the form 8k+1 and the rest of the prime factors have the form 8k+3. Products of elements in each family are shown to be non-congruent.
On the Prime Ideal of an Ordering of Higher Level.
On the prime number theorem for the coefficients of certain modular forms
On the principal congruence subgroups of the Hecke-group .
On the probability that integers chosen according to the binomial distribution are relative prime
On the probability that k generalized integers are relatively H-prime
On the probability that n and f (n) are relatively prime II
On the probability that n and f(n) are relatively prime
On the probability that n and f(n) are relatively prime III
On the probability that n and g(n) are relatively prime
On the problem of detecting linear dependence for products of abelian varieties and tori
On the problem of divisors
On the problem of Goldbach's type.
On the problem of odd h-fold perfect numbers
On the problem of uniqueness for the maximum Stirling number(s) of the second kind.
On the product ...(1-z...k).