8 In this question you must show detailed reasoning.
- Prove that \(2 ( p - 2 ) ^ { p - 2 } \equiv - 1 ( \bmod p )\), where \(p\) is an odd prime.
- Find two odd prime factors of the number \(N = 2 \times 34 ^ { 34 } - 2 ^ { 15 }\).
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\section*{OCR
Oxford Cambridge and RSA}