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|Paper IPM / M / 8066||
The aim of this paper is to prove the following statement:
noindent Let p, q be prime numbers, p ≡ 2 (mod 3), q ≡ 1 (mod 3), 4q−p2 ≡ 3 (mod 9). Suppose, furthermore, that p is not a cubic residue modulo q. Then the equation x3+y3=pqz3 has no solutions in nonzero integers x,y,z.
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