Note on the Exceptional Set in the ABC Conjecture · arXivDeskAbstract
Fix ε>0, let x>1 be a large real number and let rad(n)=∏p∣np
be the radical of an integer
. A triple
, with
and
gcd(a,b,c)=1 , such that
c>(rad(abc))1+ε , is called exceptional triple. Recent works have proved that the cardinality
#E(x) of set
of exceptional triples satisfies
#E(x)=O(x2/3) . This note proves that the cardinality of the exceptional set
of triples
is an infinite set unconditionally.