Mathematicians finally proved that a deceptively simple equation—one of the shortest ever left unsolved—has no whole-number solutions.
April 1, 2026
Original Paper
On the shortest open cubic equations
arXiv · 2603.29831
The Takeaway
While we assume simple math puzzles were solved centuries ago, this equation was the smallest cubic of its type that remained a total mystery. It took advanced number theory to prove that no combination of whole numbers can ever satisfy it, proving that even a 12-character equation can hide massive complexity.
From the abstract
We use cubic reciprocity to prove that the equation $7x^3+2y^3=3z^2+1$ has no integer solutions. Prior to this work, it was the shortest cubic equation for which the existence of integer solutions remained open. We conclude with a list of the new shortest open cubic equations.