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 delta raised to the seventh power?
Choose the correct choice from the following options.
A) alpha  B) beta  C) gamma  D) delta  E) epsilon
Let the alpha be 5k and let the delta be 5j+3.   (5k)^7 + (5j+3)^7 which has the form 5k+2, 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 delta raised to the seventh power?