This turned out to be a bit verbose, but I hope it fully answers your question… A Gaussian integer is a complex number of the form G = a+bi where i2 = -1, and a and b are integers. The Gaussian integers form a unique factorization domain. Some of them act as units (e.g. 1, … Read more
abc mod m = abc mod n mod m, where n = φ(m) Euler’s totient function. If m is prime, then n = m-1. Edit: as Nabb pointed out, this only holds if a is coprime to m. So you would have to check this first.
You got off lightly, you probably don’t want to be working for a hedge fund where the quants don’t understand basic algorithms 🙂 There is no way to process an arbitrarily-sized data structure in O(1) if, as in this case, you need to visit every element at least once. The best you can hope for … Read more