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Aug 24, 2019 at 13:11 comment added Đào Thanh Oai I have some ideas, I want private communication with you via email. But I don’t know your email, what is your email?
Aug 24, 2019 at 12:37 comment added J. E. Pascoe I can tell you that a back of the envelope calculation (probably) shows that if the $abc$-conjecture is true, then there are finitely many counterexamples. However, naive conjectures are not appropriate for mathoverflow. Problems that obviously imply big theorems should be worked on in private. The only reason I spent the 5 minutes to code this is that I thought there was some novelty in replacing $c$ by $a$ is the statement of the $abc$-conjecture. Any proof of any of the conjectures you have posted would require deep mathematics, and would not be suitable for a quick mathoverflow answer.
Aug 24, 2019 at 5:47 vote accept Đào Thanh Oai
Aug 24, 2019 at 5:44 comment added Đào Thanh Oai Can You help me check the conjecture 1 at mathoverflow.net/questions/338117 with $0< a \le b \le 10^6$
Aug 23, 2019 at 19:40 comment added J. E. Pascoe The complete list of $(a,b)$ where $a \leq b < 10000$ which violate the conjecture are $(625,2048), (1024,1377), (8019,8788), (8192,8575).$
Aug 23, 2019 at 18:42 history answered J. E. Pascoe CC BY-SA 4.0