Wyniki wyszukiwania

1

Infinite families of noncototients

100%

Flammenkamp A., Luca F.

Colloquium Mathematicum

|

2000

|

tom 86

|

nr 1

37-41

EN

For any positive integer $n$ let ϕ(n) be the Euler function of n. A positive integer $n$ is called a noncototient if the equation x-ϕ(x)=n has no solution x. In this note, we give a sufficient condition on a positive integer k such that the geometrical progression $(2^mk)_{m ≥ 1}$ consists entirely of noncototients. We then use computations to detect seven such positive integers k.

2

Two Diophantine approaches to the irreducibility of certain trinomials

81%

Filaseta M., Luca F., Stănică P., Underwood R.

Acta Arithmetica

|

2007

|

tom 128

|

nr 2

149-156

3

Minimal Niven numbers

81%

Fredricksen H., Ionascu E., Luca F., Stănică P.

Acta Arithmetica

|

2008

|

tom 132

|

nr 2

135-159

4

On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ

81%

Grytczuk A., Luca F., Wójtowicz M.

Colloquium Mathematicum

|

2000

|

tom 86

|

nr 1

31-36

EN

For any positive integer n let ϕ(n) and σ(n) be the Euler function of n and the sum of divisors of n, respectively. In [5], Mąkowski and Schinzel conjectured that the inequality σ(ϕ(n)) ≥ n/2 holds for all positive integers n. We show that the lower density of the set of positive integers satisfying the above inequality is at least 0.74.

5

Representing integers as linear combinations of S-units

81%

Ádám Z., Hajdu L., Luca F.

Acta Arithmetica

|

2009

|

tom 138

|

nr 2

101-107

Ograniczanie wyników

3 Acta Arithmetica

2 Colloquium Mathematicum

5 Luca F.

2 Stănică P.

1 Filaseta M.

1 Flammenkamp A.

1 Fredricksen H.

1 Grytczuk A.

1 Hajdu L.

1 Ionascu E.

1 Underwood R.

1 Wójtowicz M.

1 Ádám Z.

1 2009

1 2008

1 2007

2 2000

Infinite families of noncototients

Two Diophantine approaches to the irreducibility of certain trinomials

Minimal Niven numbers

On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ

Representing integers as linear combinations of S-units