Fermat Set cannot be Extended to Diophantine Quintuple

Theorem

The Fermat set $F = \set {1, 3, 8, 120}$ cannot be extended to a Diophantine quintuple.

Proof

This theorem requires a proof. In particular: Can be found in the link below. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1969: A. Baker and H. Davenport: The equations $3x^2 − 2 = y^2$ and $8 x^2 − 7 = z^2$ (Quart. J. Math. Vol. 20: pp. 129 – 137)

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $120$