## Bang (1886), Zsigmondy (1892) and Birkhoff and Vandiver (1904) initiated the study of the largest prime divisors of sequences of the form a n − b n , denoted P ( a n − b n ) , by essentially proving that for integers a > b > 0 , P ( a n − b n ) ≥ n + 1 for every n > 2.

Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes

## Denote by \$\mathbb{P}\$ the set of all prime numbers and by \$P(n)\$ the largest prime factor of positive integer \$n\geq 1\$ with the convention \$P(1)=1\$.

ON VALUES TAKEN BY THE LARGEST PRIME FACTOR OF SHIFTED PRIMES

## Let \$\$P_y^+(n)\$\$Py+(n) denote the largest prime factor p of n with \$\$p\leqslant y\$\$p⩽y.

Sur les plus grands facteurs premiers inférieur à y d’entiers consécutifs

## Results about the prime factorization of \$g(n)\$ allow a reduction of the upper bound on the largest prime divisor of \$g(n)\$ to \$1.

The Largest Prime Dividing the Maximal Order of an Element of \$S_n\$.

## Bang (1886), Zsigmondy (1892) and Birkhoff and Vandiver (1904) initiated the study of the largest prime divisors of sequences of the form a n − b n , denoted P ( a n − b n ) , by essentially proving that for integers a > b > 0 , P ( a n − b n ) ≥ n + 1 for every n > 2.

Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes

10.1016/J.DISC.2018.12.018

## • [(3)] For n ∈ N , assume that the largest prime power divisor of n is p a for some a ∈ N.

On generalized Erdős-Ginzburg-Ziv constants of Cnr

10.1017/S144678871800023X

## Denote by \$\mathbb{P}\$ the set of all prime numbers and by \$P(n)\$ the largest prime factor of positive integer \$n\geq 1\$ with the convention \$P(1)=1\$.

ON VALUES TAKEN BY THE LARGEST PRIME FACTOR OF SHIFTED PRIMES

10.1090/S0025-5718-1995-1270619-3

## Results about the prime factorization of \$g(n)\$ allow a reduction of the upper bound on the largest prime divisor of \$g(n)\$ to \$1.

The Largest Prime Dividing the Maximal Order of an Element of \$S_n\$.

10.1016/J.JNT.2019.02.016

## Bang (1886), Zsigmondy (1892) and Birkhoff and Vandiver (1904) initiated the study of the largest prime divisors of sequences of the form a n − b n , denoted P ( a n − b n ) , by essentially proving that for integers a > b > 0 , P ( a n − b n ) ≥ n + 1 for every n > 2.

Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes

10.1007/S11139-018-0110-Z

## Let \$\$P_y^+(n)\$\$Py+(n) denote the largest prime factor p of n with \$\$p\leqslant y\$\$p⩽y.

Sur les plus grands facteurs premiers inférieur à y d’entiers consécutifs

## We apply our results firstly to answer in a stronger form a question of Erdős and Pomerance on the relative orderings of the largest prime factors \$P^{+}(n)\$, \$P^{+}(n+1), P^{+}(n+2)\$ of three consecutive integers.

Value patterns of multiplicative functions and related sequences

10.7546/nntdm.2019.25.2.8-15

## Positive integers equal to the sum of powers of consecutive primes from the least prime factor to the largest prime factor are studied.

Straddled numbers: numbers equal to the sum of powers of consecutive primes from the least prime factor to the largest prime factor

10.1142/S1793042119500507

## Denote by ℙ the set of all primes and by P(n) the largest prime factor of integer n ≥ 1 with the convention P(1) = 1.

On values taken by the largest prime factor of shifted primes (II)

10.1016/J.LAA.2019.05.013

## For each n ≥ 1 , let p n be the largest prime less than or equal to n + 1.

Equality of numerical ranges of matrix powers