Linked from
The 51 pages that link to Finite field, each with the reason it gives.
Modular arithmeticBroader topic: Residues modulo a prime provide the simplest finite fields.
Field (mathematics)Broader topic: Finite fields show that field arithmetic can work on a finite set.
Field extensionBroader topic: Finite extensions of prime fields produce every finite field.
FieldBroader topic: Finite fields show that fields need not contain infinitely many elements.
Carmichael's theoremBroader topic: Its nonzero elements form a cyclic group by the theorem.