Question

for which values of n will any set of consecutive integers, each raised to the power of n and added together give a total which divides by 7?

Answer 1

Explanation:

If a number A is divisible by 7, then it satisfies the following condition

● A = 7k

k is an integer

Let A be the sum of consecutive integers raised to the power of n

● A = a^n + (a+1)^n + (a+2)^n + .....

For this sequence to be divisible by 7 it must satisfy the condition above

A = 7k where k is an integer