Abstract
In this paper, we find necessary and sufficient conditions for a weak fuzzy complex integer triple (X,Y, Z) to be a pythagoras triple, and for an anti-weak fuzzy complex integer triple to be a Pythagoras triple (X,Y, Z), where we prove that the non-linear Fermat's Diophantine equation has three different types of solutions according to the value of . All types will be solved and discussed in terms of theorems and examples that explains how the algorithms work
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