Mathematics · the experiment
Cap the sum
Three whole numbers, a + b = c, and the product N of their primes. Four questions, from beginner to expert, on the ceiling this preprint claims to set.
1 · Say what the paper claims
Beginner
What does Christophe Soulé announce in this preprint?
2 · Compute N
1 + 80 = 81, with 80 = 2⁴ × 5 and 81 = 3⁴. N is the product of the primes that divide abc, each counted once.
Intermediate
What is N for this triple?
3 · Read Theorem B
Theorem B: for every ε > 0, there is A(ε) such that, if a + b = c with no common factor, then c ≤ A(ε) · N^(24+ε).
Expert
What does this theorem say about a triple with N = 30?
4 · Change the starting factor
In the proof, the factor 12 + ε of Theorem A is multiplied by 5/2 (curve y² + y = x⁵), then by 4/5 (estimate of a discriminant): hence the exponent 24 + ε. Vojta's conjecture would put 1 + ε in place of 12 + ε.
Expert
With that factor 1 + ε, what exponent would the same chain give?
Sum capped
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