Congruence

Wednesday, 6 March 2019

10:43 AM

Two integers  and  are  denoted by

If

 

 for some integer

 

 

 

 

Consider  

 

If  - then there is a unique solution modulo

If
Then

 

 

If  is not a factor of  then the congruence has no solution

 

If  is a factor of , then the congruence has one different unique solution modulo  and  different solutions modulo m

 

 

 

 

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For   questions,

Evaluate  -->

 

Where

The GCD indicates how many solutions there are

If the GCD is not a factor of the remainder, then there is NO solution

 

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