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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Integer vectors with interprimed components


Author: Harold N. Shapiro
Journal: Math. Comp. 27 (1973), 455-462
MSC: Primary 10H15
DOI: https://doi.org/10.1090/S0025-5718-1973-0335452-0
MathSciNet review: 0335452
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Abstract: Vectors are considered whose components are positive integers. Such a vector is called interprimed if the components all contain exactly the same distinct prime factors. A method is provided for estimating the number of such vectors, all of whose components are less than a given bound. These estimates resolve a conjecture of Erdös and Motzkin.


References [Enhancements On Off] (What's this?)

  • [1] Paul Erdös & T. Motzkin, "Advanced problems, no. 5735," Amer. Math. Monthly, v. 77, 1970, p. 532. (No solution supplied by proposer.) MR 1535930
  • [2] "Advanced problems, no. 5735," Amer. Math. Monthly, v. 78, 1971, p. 680.
  • [3] G. H. Hardy & E. M. Wright, The Theory of Numbers, Oxford, 1938, Theorem 316, p. 259.

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DOI: https://doi.org/10.1090/S0025-5718-1973-0335452-0
Article copyright: © Copyright 1973 American Mathematical Society

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