Number Theory


Abc Conjecture is in the Ambiguity in Which Case of ε>0

Authors: Zhang Tianshu

Since there are infinitely many consecutive satisfactory values of ε to enable A+B=C satisfying C>(rad(A, B, C))1+ε, thus the author uses a representative equality, namely 1+2N(2N-2)=(2N-1)2 satisfying (2N-1)2>[rad(1, 2N(2N-2), (2N-1)2)]1+ε, and that first let ε equal a value near the greater end of the infinitely many consecutive satisfactory values to prove the ABC conjecture; again let ε equal a value near the smaller end to negate the ABC conjecture. This shows that the ABC conjecture is in the ambiguity in which case of ε>0.

Comments: 12 Pages.

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Submission history

[v1] 2018-12-07 21:04:48

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