Corpus ID: 237581601

Squarefree integers and the $abc$ conjecture

  title={Squarefree integers and the \$abc\$ conjecture},
  author={Zenon B. Batang},
  • Z. Batang
  • Published 18 September 2021
  • Mathematics
For coprime positive integers a, b, c, where a+ b = c, gcd(a, b, c) = 1 and 1 ≤ a < b, the famous abc conjecture (Masser and Oesterlè, 1985) states that for ε > 0, only finitely many abc triples satisfy c > R(abc), where R(n) denotes the radical of n. We examine the patterns in squarefree factors of binary additive partitions of positive integers to elucidate the claim of the conjecture. With abc hit referring to any (a, b, c) triple satisfying R(abc) < c, we show an algorithm to generate hits… Expand


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