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Mathematics 220 Homework for Week 7 Due March 6 If
Mathematics 220 Homework for Week 7 Due March 6 If

... But bc and ad are products of integers and are integers; so x is rational, which contradicts the assumption. 5.24 Prove that there exists no positive integer x such that 2x < x2 < 3x. Solution: Assume, to the contrary, that x is a positive integer with 2x < x2 < 3x. Since x is positive. 1/x is posit ...
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System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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