There are no k-th power Diophantine triples of the form {a^k, b, c} for k ≥ 3 and 1 < a^k < b < c.
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On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$
There are no k-th power Diophantine triples of the form {a^k, b, c} for k ≥ 3 and 1 < a^k < b < c.