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Kto się boi bardziej, czyli współczynnik Arrowa-Pratta

100%

Skałba M.

Matematyka Poglądowa

|

2017

|

nr 4

7-10

PL

-

2

On Euler-von Mangoldt's equation

100%

Skałba M.

Colloquium Mathematicum

|

1996

|

tom 69

|

nr 1

143-145

3

On numbers with a unique representation by a binary quadratic form

100%

Skałba M.

Acta Arithmetica

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1993

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tom 64

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nr 1

59-68

4

On Alternatives of Polynomial Congruences

100%

Skałba M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2004

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tom 52

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nr 2

123-132

EN

What should be assumed about the integral polynomials $f₁(x),...,f_{k}(x)$ in order that the solvability of the congruence $f₁(x)f₂(x) ⋯ f_{k}(x) ≡ 0 (mod p)$ for sufficiently large primes p implies the solvability of the equation $f₁(x)f₂(x) ⋯ f_{k}(x) = 0$ in integers x? We provide some explicit characterizations for the cases when $f_j(x)$ are binomials or have cyclic splitting fields.

5

Twierdzenia Fermata różnej wielkości

100%

Skałba M.

Matematyka Poglądowa

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2018

|

nr 5

13-15

PL

-

6

Towards Bauer's theorem for linear recurrence sequences

100%

Skałba M.

Colloquium Mathematicum

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2003

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tom 98

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nr 2

163-169

EN

Consider a recurrence sequence $(x_{k})_{k∈ℤ}$ of integers satisfying $x_{k+n} = a_{n-1}x_{k+n-1} + ... + a₁x_{k+1} + a₀x_{k}$, where $a₀,a₁,...,a_{n-1} ∈ ℤ$ are fixed and a₀ ∈ {-1,1}. Assume that $x_{k} > 0$ for all sufficiently large k. If there exists k₀∈ ℤ such that $x_{k₀} < 0$ then for each negative integer -D there exist infinitely many rational primes q such that $q|x_{k}$ for some k ∈ ℕ and (-D/q) = -1.

7

Products of disjoint blocks of consecutive integers which are powers

100%

Skałba M.

Colloquium Mathematicum

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2003

|

tom 98

|

nr 1

1-3

EN

The product of consecutive integers cannot be a power (after Erdős and Selfridge), but products of disjoint blocks of consecutive integers can be powers. Even if the blocks have a fixed length l ≥ 4 there are many solutions. We give the bound for the smallest solution and an estimate for the number of solutions below x.

8

Linear recurrences as sums of squares

88%

Skałba M.

Acta Arithmetica

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2012

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tom 155

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nr 2

207-216

9

Relations between polynomial roots

64%

Drmota M., Skałba M.

Acta Arithmetica

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1995

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tom 71

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nr 1

65-77

10

Relations between polynomial roots

23%

Drmota M., Skałba M.

Acta Arithmetica

|

1995

|

tom 71

|

nr 1

64-77

Ograniczanie wyników

4 Acta Arithmetica

3 Colloquium Mathematicum

2 Matematyka Poglądowa

1 Bulletin of the Polish Academy of Sciences. Mathematics

10 Skałba M.

2 Drmota M.

1 2018

1 2017

1 2012

1 2004

2 2003

1 1996

2 1995

1 1993

Kto się boi bardziej, czyli współczynnik Arrowa-Pratta

On Euler-von Mangoldt's equation

On numbers with a unique representation by a binary quadratic form

On Alternatives of Polynomial Congruences

Twierdzenia Fermata różnej wielkości

Towards Bauer's theorem for linear recurrence sequences

Products of disjoint blocks of consecutive integers which are powers

Linear recurrences as sums of squares

Relations between polynomial roots

Relations between polynomial roots