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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