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Math · Advanced Math
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Exercise 2. Let p be a prime number, and put the following multiplication and addition on [0,... ,p-13. To add two elements, add them as integers, and then take the remainder when dividing by p. To multiply two elements, multiply them as integers and then take the remainder when dividing by p This object is called Fp (1) Show that Fp is a field. (Hint: To show the existence of a multiplica- tive inverse feel free to use the fact that if a and b are integers with no prime factors in common, then there are integers x and y so that ax + by = 1·) (2) We could put a similarly defined multiplication and addition on (0,...,n - 1, where n is not prime. Will this ever form a field? How many of the field axioms does this satisfy?
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