Squarefree integers and the $abc$ conjecture

For coprime positive integers $a, b, c$, where $a+b=c$, $\gcd(a,b,c)=1$ and $1\leq a 0$, only finitely many $abc$ triples satisfy $c > R(abc)^{1+\varepsilon}$, 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)

Keywords:

• Binary number
• Mathematics
• abc conjecture
• Combinatorics
• Conjecture
• Integer
• Square-free integer
• Coprime integers

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