Wilson's Theorem

Questions involving Wilson's Theorem to test primality or find factorial values modulo primes.

3 questions · Standard +0.9

Sort by: Default | Easiest first | Hardest first
OCR Further Additional Pure 2019 June Q8
11 marks Hard +2.3
8 In this question you must show detailed reasoning.
  1. Prove that \(2 ( p - 2 ) ^ { p - 2 } \equiv - 1 ( \bmod p )\), where \(p\) is an odd prime.
  2. Find two odd prime factors of the number \(N = 2 \times 34 ^ { 34 } - 2 ^ { 15 }\). \section*{END OF QUESTION PAPER} \section*{OCR
    Oxford Cambridge and RSA}
AQA Paper 2 2018 June Q5
2 marks Easy -2.0
Prove that 23 is a prime number. [2 marks]
OCR Further Additional Pure 2018 September Q5
11 marks Hard +2.3
  1. You are given that \(N = \binom{p-1}{r}\), where \(p\) is a prime number and \(r\) is an integer such that \(1 \leq r \leq p - 1\). By considering the number \(N \times r!\), prove that \(N \equiv (-1)^r \pmod{p}\). [5]
  2. You are given that \(M = \binom{2p}{p}\), where \(p\) is an odd prime number. Prove that \(M \equiv 2 \pmod{p}\). [6]