# The fifth power

Number Theory Level pending

Let $$P(n)=n^5-n$$ be a function defined for positive integers $$n$$. Which of the following statements are true for all $$n$$.

[1] $$P(n) \mod (n+1) = 0$$

[2] $$P(n) \mod 10 = 0$$

[3] $$P(n) \mod (n^2+1) = 0$$

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