Find all residues $a$ such that $a$ is its own inverse modulo $317.$ (Your answer should be a list of integers greater than 0 and less than $317,$ separated by commas.)

Guest Sep 8, 2017

1+0 Answers


To solve for the value of the residues A, we can use the formula:

A^2 = 1                 (mod prime)

This is only true for prime numbers. The given number which is 317 is a prime number therefore the values of the residues A are:

A = + 1, - 1

Since I believe the problem specifically states for the list of positive integers only and less than 317, a value of A = - 1 is therefore not valid. However, a value of – 1 in this case would simply be equal to:

317 – 1 = 316


Therefore the residue values A are 1 and 316.

cowgirlkatie03  Sep 8, 2017

17 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details