Show that if a is an integer, then 3 divides (a to the power 3) - a I don't know how to use the mathematical software to express the question, I apologize for any inconvenience. Thanks for helping me out.
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Originally Posted by suedenation Show that if a is an integer, then 3 divides (a to the power 3) - a I don't know how to use the mathematical software to express the question, I apologize for any inconvenience. Thanks for helping me out. a^3-a=a(a^2-1)=a(a-1)(a+1) that is it is the product of three consecutive integers. But in every set of three consectutive integers at least one is divisible by 3. Hence a^3-a is divisible by 3. RonL
Furthermore, this is a faboulus beautiful elegant powerful super and amazing theorem of Fermat (my favorite mathemation). That, a^p-a Is always divisible by p
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