On the sum ... D(n) ... (n + N).
On the sum of a prime and the kth power of a prime
On the sum of consecutive cubes being a perfect square
On the sum of digits of some sequences of integers
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
On the sum of dilations of a set
We show that for any relatively prime integers 1 ≤ p < q and for any finite A ⊂ ℤ one has .
On the sum of divisors of the Mersenne numbers
On the sum of iterations of the Euler function.
On the sum of the first n values of the Euler function
Let ϕ(n) be the Euler function of n. We put and give an asymptotic formula for the second moment of E(n).
On the sum of the number of divisors in a short segment
On the sum of two integral squares in quadratic fields ℚ(√±p)
On the sum of two squares and two powers of k
It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2.
On the Sum-of-Divisors Function of the Numbers of Fermat and Ferentinou-Nicolacopoulou
On the sums ... .
On the sums of continued fractions
On the sums
On the sumset of the primes and a linear recurrence
Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.
On the Supercuspidal Represewntations of SL2 and ist Two-fold Cover. II.
On the Supercuspidal Represewntations of SL2 and ist Two-fold Cover. I
On the surjectivity of Galois representations attached to elliptic curves over number fields
On the switching principle in sieve theory.