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- Thread starter matqkks
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Ssnow

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In mathematics they are used for the computation of Legendre symbols and for the proof when a number is expressible as sum of two squares ...

Ssnow

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Stephen Tashi

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They have done Diophantine equations, solved linear congruences

If the class has studied linear congruences then purely mathematical curiosity leads to asking about polynomial congruences. The simplest example would be ##x^2 = A (mod\ M)## I haven't studied this topic. A blog by John Cook https://www.johndcook.com/blog/quadratic_congruences/ deals with it.

I wonder if any application of quadratic residues to a practical topic comes by way of needing to solve ##x^2 = A (mod \ M)##.

primitive roots.

The solutions to the quadratic equation ##x^2 = -1## play a crucial role in the theory of solving general polynomial equations over the real numbers. I wonder if the solutions to ##x^2 = A (mod\ N)## play a crucial role in the theory of solving general polynomial equations over the integers in mod N arithmetic. Can anybody comment on that?

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