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University math. Show full answer. Answer within 2 hours Q5 (10 points) Show that in any field F, the equation 2 = 1 can have

University math. Show full answer. Answer within 2 hours

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Q5 (10 points) Show that in any field F, the equation 2 = 1 can have at most two solutions. Can you think of a field in which the equation a = 1 has exactly one solution?Q6 (10 points) Construct a field with 5 elements. Draw the tables of addition and multiplication. Hint 1. Let the elements of such a field be {0, 1, a, b, c}. Hint 2. use the cancellation rules, you may use the axioms and claim/propositions about fields in the course notes. You do not need to write all the reasoning only drawing the tables for addition and multiplication is enough (but make sure to understand the reasoning)

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