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Which of the following numbers can be the order (i.e., the number of elements) of a finite field?

A. 19
B. 24
C. 118
D. 242
E. 293
F. 881
G. 78
H. 151
I. 773
J. 220

Answer :

Final answer:

The numbers that can be the order of a finite field are 19, 151, and 773.

Explanation:

A finite field is a mathematical structure that consists of a finite set of elements along with two operations, addition and multiplication. The order of a finite field is the number of elements it contains.

In order for a number to be the order of a finite field, it must be a prime number or a power of a prime number. This is because the order of a finite field must be a prime or a power of a prime due to the properties of finite fields.

For example, if a finite field has order p^n, where p is a prime number and n is a positive integer, then the field can be constructed as an extension of the finite field with order p. In this case, the field with order p^n is called an extension field of the field with order p.

Based on this, the numbers that can be the order of a finite field from the given options are:

  • 19
  • 151
  • 773

Learn more about finite fields here:

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