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math.GM2026
Integers representable as a difference of two rational fourth powers
Ashleigh Ratcliffe, Tho Nguyen Xuan
In Section 6.6 of the book {\it Number Theory, Volume I: Tools and Diophantine Equations, Graduate Texts in Mathematics, Volume 239, Springer (2007)}, Cohen investigated the solubi…
math.GM2026
On the shortest open cubic equations
Bogdan Grechuk, Ashleigh Ratcliffe
We use cubic reciprocity to prove that the equation has no integer solutions. Prior to this work, it was the shortest cubic equation for which the existence of i…