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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

How many invertible 2×22\times2 matrices are there over the field F5\mathbb{F}_{5} (that is, ∣GL2(F5)∣|GL_2(\mathbb{F}_{5})|)?