right or wrong

Show that a^x+a and a^x-a are always even whatever a and x may be

I did it by taking four cases for a and x [EE,EO,OE,OO] where E and O denote even and odd respectively

Is any shorter method available ?

2 Answers

Divisibility by 2 shall be influenced only by a here, not by x, so from F.L.t.....a^k-1â‰¡0(mod2), for all k.....and a......

yes
whatever may be x

any power of odd number will be odd
and any power of even number will be even.

I got your point.Thank you :-)

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