How do I prove that 5 divides x^5 - x?

  • #1
How do I prove that 5 divides x^5 - x??

How do I prove that 5 divides x^5 - x??
 

Answers and Replies

  • #2
CRGreathouse
Science Advisor
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Compute the fifth powers mod 5.
 
  • #3
CompuChip
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Let me give you a hint: checking it for x = 0, 1, 2, 3 and 4 suffices.

(In fact, as 4 = -1 (mod 5) and 3 = -2 (mod 5), you can see that only x = 0, 1, 2 will do).

I'll let you figure out why.
 

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