public static long Solution()
{
long solution = 0;
long mLimit = (long)1e4;
HashSet <long> squares = new HashSet <long>();
for (long m = 2; m < mLimit; m++)
{
long kLimit = (long)Math.Sqrt(limit / (m * m * m) + 1);
var step = 2 - (m % 2);
for (long r = 1; r < m; r += step)
{
if (UtilityFunctions.Gcd(m, r) != 1)
{
continue;
}
if (m * m * m * r + r * r >= limit)
{
break;
}
for (long k = 1; k <= kLimit; k++)
{
long n = k * k * m * m * m * r + k * r * r;
if (n >= limit)
{
break;
}
if (UtilityFunctions.IsPerfectSquare(n))
{
if (!squares.Contains(n))
{
solution += n;
squares.Add(n);
}
}
}
}
}
return(solution);
}
public static long Solution()
{
long solution = 0;
for (int a = 1; a <= limit; a++)
{
for (int c = 1; c <= a; c++)
{
for (int b = 1; b <= limit; b++)
{
for (int d = 1; d <= b; d++)
{
var internalPoints =
((a + c) * (b + d)
- UtilityFunctions.Gcd(a, b)
- UtilityFunctions.Gcd(b, c)
- UtilityFunctions.Gcd(c, d)
- UtilityFunctions.Gcd(d, a)) / 2 + 1;
if (UtilityFunctions.IsPerfectSquare(internalPoints))
{
solution += 4;
if (a == c || b == d)
{
solution -= 2;
if (a == c && b == d)
{
solution -= 1;
}
}
}
}
}
}
}
return(solution);
}
public static long SolutionOld()
{
long answer = 0;
var validPairs = new Dictionary <long, HashSet <long> >();
var validSums = new HashSet <long>();
for (long p = 2; p < limit; p++)
{
for (long q = 1; q < p; q++)
{
if (p + q > limit)
{
break;
}
if (p % 2 == 1)
{
if ((q % 2 == 1) && (p * q) % 4 != 3)
{
continue;
}
if (q % 4 == 2)
{
continue;
}
}
else
{
if ((p % 4 == 2) && (q % 2 == 1))
{
continue;
}
}
var aSquare = (p * p + q * q + p * q);
if (!UtilityFunctions.IsPerfectSquare(aSquare))
{
continue;
}
if (validPairs.ContainsKey(p))
{
validPairs[p].Add(q);
if (validPairs.ContainsKey(q))
{
long sum = long.MaxValue;
foreach (var r in validPairs[q])
{
if (validPairs[p].Contains(r))
{
var bSquare = p * p + r * r + p * r;
var cSquare = r * r + q * q + r * q;
if (bSquare + cSquare < aSquare)
{
var bc = Math.Sqrt(bSquare * cSquare);
if (bSquare + cSquare + bc < aSquare)
{
continue;
}
}
sum = p + q + r;
if (sum < limit)
{
validSums.Add(sum);
Console.WriteLine($"{p} {q} {r} {sum}");
}
}
}
}
}
else
{
validPairs.Add(p, new HashSet <long> {
q
});
}
}
}
foreach (var sum in validSums)
{
answer += sum;
}
return(answer);
}
