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 a gamma raised to the seventh power?
Choose the correct option: A) alpha B) beta C) gamma D) delta E) epsilon
Let the alpha be 5k and let the gamma be 5j+2.   (5k)^7 + (5j+2)^7 which has the form 5k+3, which is a gamma.   The answer is gamma.
<result>C</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 a gamma raised to the seventh power?