Abstract:

We give a sketch of Jacobi's proof that the number of ways in which a positive integer can be written as a sum of four squares is equal to eight times the sum of those divisors which are not divisible by four. This proof using elliptic functions originally appears in Jacobi's Fundamenta Nova [Jacobi1829].

Jacobi's Four Square Theorem

Eric Conrad

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Email: econrad@math.ohio-state.edu