Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
using System; using System.Collections.Generic; using System.Diagnostics; namespace Project_Euler_29 { internal class Program { private static void Main(string[] args) { Stopwatch sw = Stopwatch.StartNew(); HashSet<double> results = new HashSet<double>(); for (int a = 2; a <= 100; a++) { for (int b = 2; b <= 100; b++) { results.Add(Math.Pow(a, b)); } } sw.Stop(); Console.WriteLine($"Number of distinct powers: {results.Count}"); Console.WriteLine($"Took {sw.ElapsedMilliseconds}ms"); } } }
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