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.
- G. G. Lorentz, Paul Erdos, T. Motzkin, M. S. Klamkin, Simeon Reich, E. M. Reingold, and Richard Johnsonbaugh, Problems and Solutions: Advanced Problems: 5734-5739, Amer. Math. Monthly 77 (1970), no. 5, 532–533. MR 1535930, DOI 10.2307/2317403 "Advanced problems, no. 5735," Amer. Math. Monthly, v. 78, 1971, p. 680. G. H. Hardy & E. M. Wright, The Theory of Numbers, Oxford, 1938, Theorem 316, p. 259.
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 455-462
- MSC: Primary 10H15
- DOI: https://doi.org/10.1090/S0025-5718-1973-0335452-0
- MathSciNet review: 0335452