Final answer:
The statement is true because if d, the greatest common divisor of a and n, does not divide b, then there are no integer solutions for the congruence ax ≡ b mod n.
Step-by-step explanation:
The question pertains to a statement in number theory which is a part of mathematics. It says that given the integers a, x, b, and n, with d being the greatest common divisor of a and n (d=(a,n)), if a congruence relation ax ≡ b mod n is given and d does not divide b, then there are no integer solutions for x. This statement is true. If d divides a, it must also divide any multiple of a, including ax for any integer x. Therefore, if d does not divide b, then ax cannot be congruent to b mod n, since the left side of the congruence would have d as a factor while the right side would not, making equality impossible.