Show that the function pk klkc is a permutation of the set

Show that the function p(k) = k+(-l)^kc is a permutation of the set of all integers, whenever c is an integer.

Solution

p(k) = k-kc = k(1-c)

for different values of k, p(k) will attain different values of integers provided c is an integer other than 1. It is quite evident from the equation itself