7 Throughout this question, \(n\) is a positive integer.
- Explain why \(n ^ { 5 } \equiv n ( \bmod 5 )\).
- By proving that \(n ^ { 5 } \equiv n ( \bmod 2 )\), show that \(n ^ { 5 } \equiv n ( \bmod 10 )\).
- Prove that \(n ^ { 5 } - n\) is divisible by 30 for all positive integers \(n\).
- Is there an integer \(N\), greater than 30 , such that \(n ^ { 5 } - n\) is divisible by \(N\) for all positive integers \(n\) ? Justify your answer.