# Find all solutions of x2 + x +1 ≡ 0 (mod 11) etc..

Number Theory - Polynomial Congruences

Find all solutions of each of the following congruences .
(a) x2 + x +1 &#8801; 0 (mod 11)
(b) x3 + x + 1 &#8801; 0 (mod 13)
(c) x4 + x3 + 2 &#8801; 0 (mod 7)

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• question of the Polynomial Congruences.doc
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Solution Summary

This solution is comprised of a detailed explanation for solving the problems on polynomial congruences.
It contains step-by-step explanation for finding all solutions of each of the following congruences:
(a) x2 + x +1 &#8801; 0 (mod 11)
(b) x3 + x + 1 &#8801; 0 (mod 13)
(c) x4 + x3 + 2 &#8801; 0 (mod 7)

Solution contains detailed step-by-step explanation.

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Thokchom Sarojkumar Sinha, MSc

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Active since 2006

BSc, Manipur University
MSc, Kanpur University

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Extracted Content from Question Files:

• question of the Polynomial Congruences.doc

Find all solutions of each of the following congruences .
(a) x2 + x +1 ≡ 0 (mod 11)
(b) x3 + x + 1 ≡ 0 (mod 13)
(c) x4 + x3 + 2 ≡ 0 (mod 7)