| viXra.org > Number Theory > viXra:2605.0115 |
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| viXra.org > Number Theory > viXra:2605.0115 |
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Number Theory |
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Authors: J.W.L. Eerland
In an earlier paper I considered the generalized cannonball problem for r-regular polygons and studied integer solutions to the associatedDiophantine equation. In this note I prove that for every positive integer n, the triple[(r,a,b)=left(3n+2,,3n^2-2,,3n^3-3n+1ight)] is a solution. Hence the generalized cannonball problem admits infinitely many positive integer solutions. I also compare this parametric family with the 858 tuples listed in the appendix of the earlier paper. Among those tuples, 802 are generated by the present family and the remaining 56 tuples are listed explicitly.
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[v1] 2026-05-31 18:39:00
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