# Fermat Set cannot be Extended to Diophantine Quintuple

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## Theorem

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

## Proof

## 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**: 129 – 137)

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