TY - JOUR
T1 - On the parity of exponents in the factorization of n!
AU - Berend, Daniel
N1 - Funding Information:
* Research supported in part by the Basic Research Foundation. -E-mail: berend black.bgu.ac.il.
PY - 1997/1/1
Y1 - 1997/1/1
N2 - It is shown that, for any k, there exist infinitely many positive integers n such that in the prime power factorization of n!, all first k primes appear to even exponents. This answers a question of Erdös and Graham ("Old and New Problems and Results in Combinatorial Number Theory," L'Enseignement Mathématique, Imprimerie Kundia, Geneva, 1980). A few generalizations are provided as well.
AB - It is shown that, for any k, there exist infinitely many positive integers n such that in the prime power factorization of n!, all first k primes appear to even exponents. This answers a question of Erdös and Graham ("Old and New Problems and Results in Combinatorial Number Theory," L'Enseignement Mathématique, Imprimerie Kundia, Geneva, 1980). A few generalizations are provided as well.
UR - http://www.scopus.com/inward/record.url?scp=0031139068&partnerID=8YFLogxK
U2 - 10.1006/jnth.1997.2106
DO - 10.1006/jnth.1997.2106
M3 - Article
AN - SCOPUS:0031139068
SN - 0022-314X
VL - 64
SP - 13
EP - 19
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -