Some remarks on the $abc$-conjecture
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- by J. Browkin and J. Brzeziński PDF
- Math. Comp. 62 (1994), 931-939 Request permission
Abstract:
Let $r(x)$ be the product of all distinct primes dividing a nonzero integer x . The abc-conjecture says that if a, b, c are nonzero relatively prime integers such that $a + b + c = 0$, then the biggest limit point of the numbers \[ \frac {{\log \max (|a|,|b|,|c|)}}{{\log r(abc)}}\] equals 1. We show that in a natural anologue of this conjecture for $n \geq 3$ integers, the largest limit point should be replaced by at least $2n - 5$. We present an algorithm leading to numerous examples of triples a, b, c for which the above quotients strongly deviate from the conjectural value 1.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp. 62 (1994), 931-939
- MSC: Primary 11D04; Secondary 11A55, 11Y65
- DOI: https://doi.org/10.1090/S0025-5718-1994-1218341-2
- MathSciNet review: 1218341