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The "Diophantine" property of the zeros of certain polynomials in the Askeyscheme, recently discovered by Calogero and his collaborators, is explained,with suitably chosen parameter values, in terms of the summation theorem ofhypergeometric series. Here the Diophantine property refers to integer valuedzeros. It turns out that the same procedure can also be applied to polynomialsarising from the basic hypergeometric series. We found, with suitably chosenparameters and certain $q-$analogue of the summation theorems, zeros of thesepolynomials explicitly, which are no longer integer valued. This goes beyondthe results obtained by the Authors mentioned above.

Hypergeometric Origins of Diophantine Properties Associated With the Askey Scheme