If \(k\) is a positive integer, what is the remainder when \(62^{k^3}\) is divided by \(7?\)

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If \(k\) is a positive integer, what is the remainder when \(62^{k^3}\) is divided by \(7?\)

(1) \(k\) is an even integer.

(2) \(k^3\) is divisible by \(82.\)

Answer: D

Source: e-GMAT