<PRE><B>Question 6689</B>
 Solve
 233 x = 219 (mod 792)
 Since 792 and 233 are relative prime(in fact 233 is prime)
 
 USe Euclidan algorithm to find the inverse of 233 in mod 792
 792  = 233 * 3 + 93,
 233 = 93*2 + 47,
 93 = 47*2 - 1
 
 Hence, -1 = 93 - 47*2
           = 93 - (233 -93*2)*2
           = 233*(-2) + 93*5
           = 233*(-2) + (792 -233*3)*5
           = 233*(-17) + 792*5

 Or 233*17 + 792*(-5) = 1

 Apply mod 792 on both sides, we have 233*17 = 1 mod 792.
 This means 17 is the inverse of 233 mod 792.
 Multiply 17 on both sides of 233 x = 219 (mod 792) , we get
 x = 17* 219 mod 792 = 555 mod 792.

 Use Excel, check  MOD(233*555,792) = 219 OK
 The answer x = 555 mod 792.
 
 Kenny


</PRE>