We use the recent evaluation of certain convolution sums involving the sum of divisors function to determine the number of representations of a positive integer by certain diagonal octonary quadratic forms whose coefficients are 1, 2 or 4.

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International Journal of Number Theory
School of Mathematics and Statistics

Alaca, A, Alaca, S, & Williams, K.S. (2010). Fourteen octonary quadratic forms. International Journal of Number Theory, 6(1), 37–50. doi:10.1142/S179304211000279X