Suppose o:Z50 - Z15 is a homomorphism with Þ(7) = 6. (i) Determine p(x) where x € Z50. Hint: Use the fact that 7 23 =1 (mod 50). It follows that 7x = y (mod 50), then x = 43y (mod 50). (ii) Determine the kernel of o.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.