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 a gamma raised to the seventh power and a delta raised to the seventh power?
Choose the correct answer
A) alpha
B) beta
C) gamma
D) delta
E) epsilon
Solution : 2 is gamma and 3 is a delta. 2^7 + 3^7 will have a units digit as 8+7=5. So, label is alpha.   or   alpha : 5k   beta : 5k +1   gamma : 5K+2   delta : 5k+3   epsilon : 5K+4   (5k + 2)^7 has unit digit as 8 or 3   (5k + 3)^7 has unit digit as 7 or 2   In any case (5k + 2)^7 + (5k + 3)^7 will have units digit as 0 or 5 which is a alpha.   Option alpha
<result>A</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 a gamma raised to the seventh power and a delta raised to the seventh power?