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nadezda [96]
3 years ago
9

Find all residues (A) such that (A) is its own inverse modulo 317.

Mathematics
1 answer:
marta [7]3 years ago
8 0

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

<span>A^2 = 1                 (mod prime)</span>

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

 

<span>Therefore the residue values A are 1 and 316.</span>

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