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The problem of determining cyclotomic numbers in terms of the solutions ofcertain Diophantine systems has been treated by many authors since the age ofGauss. In this paper we obtain an explicit expression for cyclotomic numbers oforder 2l^2 in terms of the coefficients of the Jacobi sums of lower orders. Atthe end, we illustrate the nature of two matrices corresponding to two types ofcyclotomic numbers.

Cyoclotomic Numbers Of Order 2l^2 With Prime L