Question

If there is a unique prime number p1 then a finite field F has the property of ______________

(a) p1x = 0 for all x in F

(b) f(x) = f(xp1) for all x in F

(c) p1 = y for all y in F

(d) xy + p1 for all x, y in F

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This is a very interesting question from Number Theory topic in section Number Theory and Cryptography of Discrete Mathematics

Answer 1

Correct answer is (a) p1x = 0 for all x in F

To elaborate: A field can be defined as an algebraic structure in which multiplication, addition, subtraction, and division are well-defined and satisfy similar properties. If there is a unique prime number p1 then a finite field F has the property of p1x = 0, for all x in F and this prime number is called the characteristics of the field.