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**Szpieg** -Show that x-a is a factor of x^n-a^n for any positive integer n.

-Show that x+a is a factor of x^n+a^n for any positive odd integer n.

-Prove that if a≠b, then (a, b) and (b, a) lie on a line perpendicular to the line y=x and are equidistant from y=x.

-Prove that if f is a one-to-one odd function, f-^-1 is an odd function.

-Consider the following system of equations in x+y:

ax+by=c

dx+ey=f

Where the constants a, b, c, d, e, and f form an arithmetic sequence. How might you characterize the solutions to the system of equations?