IGNOU BMTC 134 2026 - Construct a field with 125 elements.

Question

Construct a field with 125 elements. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$

10 Jan 2026

Answer :

Word Count : 168

A field with 125 elements must have order (125 = 5^3), so it is a finite field of characteristic 5. Denote it by (\mathbb{F}_{5^3}). Start with the prime field (\mathbb{F}*5 = {0,1,2,3,4}). To construct (\mathbb{F}*{5^3}), we need

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