Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and an epsilon raised to the seventh power?  Choose one:
A) alpha
B) beta
C) gamma
D) delta
E) epsilon
Let the alpha be 5k and let the epsilon be 5j+4.   (5k)^7 + (5j+4)^7 which has the form 5k+4, which is an epsilon.   The answer is epsilon.
<result>E</result>
Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and an epsilon raised to the seventh power?