Exercise
Consider the system of equations x = 459 mod 241 and x = 241 mod 459. A solution to this system is
700
3718
There is no solution
Of course, since 700 = 459 + 241
I think you've guessed that one.Try to use the special form of these equations
According to the Chinese remainder theorem a sufficient condition for solvability is that gcd(459,241) = 1. In this case you may perhaps do without