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Prove Wilson's Theorem, i.e. (p-1)! = -1 (mod p) for any prime number p.

Claim : For any prime p: (p-1)! = -1 (mod p) Proof: For p=2: 1! = 1 so the equality obviously holds. Therefore, we need to consider cases when p is odd. Let's consider set: {1, ... , p-1}. With operation * m...
MP
Answered by Mateusz P. • Maths tutor
8119 Views

Explain how carbon is cycled in the environment, including the role of all living organisms and the use of fossil fuels.

This question was taken from a recent past paper.Let's start by working out what the examiner is looking for here. This question makes it quite obvious, as it states the words 'carbon' and 'cycle', telling y...
AP
Answered by Adele P. • Biology tutor
6005 Views

What is hydrogen bonding and why does water have a higher boiling point than methanol?

Hydrogen bonding is an intermolecular interaction between a partially positively charged hydrogen atom on one molecule and a partially negatively charged atom on another molecule. The difference in charge is...
MQ
Answered by Max Q. • Chemistry tutor
28836 Views

How can you tell a cell is an animal and not a plant cell?

Animal cells and plant cells contain structures, called organelles. (ask student what an organelle is; a specialised micro-structure within a cell that has a specific function) Some of these organelles are c...
HA
Answered by Hidaya A. • Biology tutor
7543 Views

How does Shakespeare present the relationship between Othello and Iago?

In his play 'Othello', Shakespeare portrays the relationship between the eponymous Othello and the Machiavellian Iago in a dramatic and compelling way. His subtle, yet powerful use of language, as well as hi...
CG
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