Infinitude conjecture for μ\mu-hits

A μ\mu-hit is an abcabc-hit in the class defined earlier in the paper; in particular, it is a coprime positive-integer triple (a,b,c)(a,b,c) with a+b=ca+b=c satisfying the paper's μ\mu-hit condition.

Infinitude conjecture for μ\mu-hits. There are infinitely many μ\mu-hits.

The paper presents this as a conjectural consequence of the expected infinitude of Wieferich primes. The preceding theorem proves that infinitely many Wieferich primes would imply infinitely many μ\mu-hits, but the infinitude of Wieferich primes is itself not known.

Sources & referencesView supporting material

Primary source

Olivier Rozier, “Are the Collatz and abc conjectures related?”, arXiv:2306.15284 (2025).

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