Let Z_36 be generated by x. For which integers n does the map f_n : 1bar to x^n extend to a well-defined homomorphism from Zmod48 to Z_36?
If I understand this correctly, to check that f_n is well-defined I need to take two elements of 1bar, say e1 and e2, and then show that x^e1=x^e2. But I can't get that to work out. Any guidance would be greatly appreciated!