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We prove an asymptotic formula for the average number of solutions to the Diophantine equation axyxy=n in which a is fixed and n varies.

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86 577 – 579 10.2307/2320589 . [4] Kannappan , Pl. 2003 Rudin’s problem on groups and a generalization of mean value theorem

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, O. M. 1999 Mean value theorems for a class of Dirichlet series J. Math. Sci. (New York) 157 659 – 672 . [5

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Acta Math. Hungar. 91 99 – 113 10.1023/A:1010687011674 . [5] Bramble , J. H. , Payne , L. E. 1966 Mean value theorems for polyharmonic functions Amer

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] Ingham , A. E. 1928 Mean-value theorems in the theory of the Riemann zeta-function Proc. Lond. Math. Soc. 27 273 – 300 10.1112/plms/s2

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