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For any prime number p, there is also the multiplicative group of integers modulo p. Its elements are the integers 1 to p 1. The group operation is multiplication modulo p. That is, the usual product is divided by p and the remainder of this division is the result of modular multiplication. For example, if p = 5, there are four group elements 1, 2, 3, 4. In this group, 4 4 = 1, because the usual product 16 is equivalent to 1, which divided by 5 yields a remainder of 1. for 5 divides 16 1 = 15, denoted

How many group elements exist if p=5?
Answer: four group elements
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In January 2008 the Wapping presses printed The Sun for the last time and London printing was transferred to Waltham Cross in the Borough of Broxbourne in Hertfordshire, where News International had built what is claimed to be the largest printing centre in Europe with 12 presses. The site also produces The Times and Sunday Times, Daily Telegraph and Sunday Telegraph, Wall Street Journal Europe (also now a Murdoch newspaper), London's Evening Standard and local papers. Northern printing had earlier been switched to a new plant at Knowsley on Merseyside and the Scottish Sun to another new plant at Motherwell near Glasgow. The three print centres represent a 600 million investment by NI and allowed all the titles to be produced with every page in full colour from 2008. The Waltham Cross plant is capable of producing one million copies an hour of a 120-page tabloid newspaper.

Where had northern printing been moved to?
Answer: Knowsley on Merseyside
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Feynman diagrams are now fundamental for string theory and M-theory, and have even been extended topologically. The world-lines of the diagrams have developed to become tubes to allow better modeling of more complicated objects such as strings and membranes. Shortly before his death, Feynman criticized string theory in an interview: "I don't like that they're not calculating anything," he said. "I don't like that they don't check their ideas. I don't like that for anything that disagrees with an experiment, they cook up an explanationa fix-up to say, 'Well, it still might be true.'" These words have since been much-quoted by opponents of the string-theoretic direction for particle physics.

What theories do Feynman diagrams help explain?
Answer:
string theory and M-theory