Claims

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1995_07_01_nitaj: Nitaj (Bull. London Math. Soc. 1995) proves that a + b = c has infinitely many solutions in coprime 3-powerful numbers, answering the third question yes with three explicit infinite families; refereed.

1998_01_01_cohn: Cohn (Math. Comp. 1998) proves that a + b = c has infinitely many solutions in pairwise coprime 3-powerful numbers none of which is a perfect cube, answering the third question yes; refereed.

2024_04_05_walsh: Walsh (Rad HAZU Mat. Znan. 2024) proves that if Y^2 = X^3 - 432p^2 has positive rank for an odd prime p, then x^3 + y^3 = p^4 z^3 has infinitely many pairwise coprime solutions; refereed, conditional on the rank.

2026_05_24_price: A manuscript shared by Liam Price, with GPT-5.5 Pro on its author line, proves infinitely many r-powerful sums of r-2 distinct jointly coprime r-powerful numbers for every r at least 6; unrefereed.

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