Partitions with equal products. II
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- by John B. Kelly
- Proc. Amer. Math. Soc. 107 (1989), 887-893
- DOI: https://doi.org/10.1090/S0002-9939-1989-0984800-0
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Abstract:
The following theorem is proved: Let $k \geq 3$ and $r$ be positive integers. There exist infinitely many integers having $r$ partitions into $k$ parts such that the products of the integers in each partition are equal. Moreover, these partitions are mutually disjoint, i.e., no integer occurs in more than one of them. Of some additional interest is a lemma stating that a certain class of elliptic curves has positive rank over ${\mathbf {Q}}$.References
- John B. Kelly, Partitions with equal products, Proc. Amer. Math. Soc. 15 (1964), 987–990. MR 168542, DOI 10.1090/S0002-9939-1964-0168542-2
- B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 33–186 (1978). With an appendix by Mazur and M. Rapoport. MR 488287, DOI 10.1007/BF02684339
- B. Mazur, Rational isogenies of prime degree (with an appendix by D. Goldfeld), Invent. Math. 44 (1978), no. 2, 129–162. MR 482230, DOI 10.1007/BF01390348
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 887-893
- MSC: Primary 11P57
- DOI: https://doi.org/10.1090/S0002-9939-1989-0984800-0
- MathSciNet review: 984800