Find all positive solutions to the equation a^3 + b^3 = c^3 + d^3 where a, b, c, and d are integers between 1 and 1000.

FindCubicSumPairs.cs

// Find all positive solutions to the equation a^3 + b^3 = c^3 + d^3
// where a, b, c, and d are integers between 1 and 1000.

FindCubicSumPairs(1, 1000).Dump();

static IEnumerable<(int A, int B, int C, int D)> FindCubicSumPairs(int min, int max)
{
    var sumToPairs = new Dictionary<double, List<(int, int)>>();
    for (int a = min; a <= max; a++)
    {
        for (int b = min; b <= max; b++)
        {
            var sum = Math.Pow(a, 3) + Math.Pow(b, 3);
            if (!sumToPairs.TryGetValue(sum, out var pairs))
                sumToPairs[sum] = pairs = new();

            pairs.Add((a, b));
        }
    }
    
    foreach (var list in sumToPairs.Values)
    {
        foreach (var (a, b) in list)
        {
            foreach (var (c, d) in list)
            {
                yield return (a, b, c, d);
            }
        }
    }
}