A simple derivation of Jacobi’s four-square formula
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- by John A. Ewell PDF
- Proc. Amer. Math. Soc. 85 (1982), 323-326 Request permission
Abstract:
For each nonnegative integer $n$, ${r_4}(n)$ counts number of solutions $({x_1},{x_2},{x_3},{x_4}) \in {{\mathbf {Z}}^4}{\text {of }}n = x_1^2 + x_2^2 + x_3^2 + x_4^2$. Within the confines of elementary partition theory the author presents a simple derivation of Jacobi’s formula for ${r_4}(n)$.References
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L. E. Dickson, History of the theory of numbers, Vol. 2, Chelsea, New York, 1952.
- John A. Ewell, Completion of a Gaussian derivation, Proc. Amer. Math. Soc. 84 (1982), no. 2, 311–314. MR 637190, DOI 10.1090/S0002-9939-1982-0637190-0 G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 323-326
- MSC: Primary 10J05; Secondary 10A45
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656093-9
- MathSciNet review: 656093