Which of the following equations have a solution?
(a) ( )
(b) ( )
(c) ( )
(d) ( )
Could anyone show me how to solve these step by step? I can't just submit my answers as 'has a solution', 'has no solution.' Thanks!
(b) Since (31,3) = 1, compute
(c) ( ) is same as ( ). Again we have (2,41) = 1. Therefore compute
(d)This one is interesting. You have to transform this quadratic congruence to linear by completing the squares and then find the quadratic residue
a) You can get this simply by a listing. No number a modulo 29 has 17 as its square. There is no solution.
and this has no solution.
Complete the square:
(Just as a note:
to both sides.)
and this has no solution for x + 13, so there is no solution for x.