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In 1924 at the Toronto meeting of the International Congress of Mathematicians, B. N. Delone introduced his empty sphere method for lattices. We have titled our paper after this method as a tribute to his memory. We have studied the sets of integer solutions of equations of the form 1 where f satisfies the following condition in which Z denotes the integers, 2 and have resolved this problem using the theory of L-types of lattices [3, 4, 11]. We have been able to give a complete description of all such integer solutions when n ≦ 4.
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Erdahl et al. (1987) studied this question.
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