Thanks for your feedback. But I very much doubt that it can be solved in O(1). Because the answers grow with increasing values of relatively prime n and m. If you wanted to ask that there is a function that would use only standard arithmetic operations and return an answer, then I don’t know. If you look at the graph, it looks very chaotic. But you can learn more about this problem here https://oeis.org/A323472.

When you have a N-dimensional array, you should use N indices if you want to get a value. For this case:
return matrix[0][0]

I am very pleased to read this, thank you. In this kata, I have a problem with parametrization by limiting the values of the parameters n and m. Because these restrictions are not enough:

0 < n < m
n / m < 1/4

If values of n or m are too large, the calculations will take too long.

Thanks for the advice, I fixed it.

If the numbers are too large, the calculation time is too fast.

I've corrected the order of the conditions, so I hope it's clearer. Thanks for the correction.

Added restrictions on arguments

Fixed.

Added.