Request for a reference

Consider the following equiation under the given conditions.

x^k + y^k = Ek^R (1)

Conditions: x, y, k, E, R are all integers each > 0
x, y are odd, k is a prime > 5, E is even.

Assertion: (1) cannot be satisfied under the given conditions.

If the assertion is correct I would appreciate some relevant
reference.
.

Relevant Pages

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