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... ut in a tactful way. But because he needed to rest, he didn't bother to spend time making his words more polite.

Of course, although the five-hundred-page paper did not succeed in proving the ABC conjecture in his opinion, it did not mean that the past two days were wasted.

Compared to the previous paper he found on the website of the department of mathematics of Kyoto University, this revised version had been optimized in many ways.

Although there were still many problems, ...

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