Not actually for homework, but i didn't know where to post this.
Problem: Show that any integer to the fourth power can be expressed as either 5k or 5k+1 where k is an integer.
The Attempt at a Solution
My starting point is to consider that all integers can be expressed as either:
2x or 2x+1
taking these to the fourth power I arrive at:
16k or 16k + 1
now i'm stuck, any tips? am i even on the right trail here?