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On the exponents modulo 3 in the standard factorisation of n!

Published online by Cambridge University Press:  17 April 2009

Wei Liu  and
Yong-Gao Chen
Wei Liu
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China, e-mail: ygchen@njnu.edu.cn
Yong-Gao Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China, e-mail: ygchen@njnu.edu.cn
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Let p be a prime and m be a positive integer. For a positive integer n, let ep(n) be the nonnegative integer with pep(n) | n and pep(n)+1 ∤ n. As a corollary of our main result we derive an asymptotic formula for the counting function with regard to the condition ep(n!) ≡ ɛ (mod 3), where ɛ ∈ Z3. In 2001, Sander proved the result with modulus 2.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 3 , June 2006 , pp. 329 - 334
Copyright
Copyright © Australian Mathematical Society 2006

References

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