// For: https://forum.arduino.cc/t/does-arduino-have-limitations-with-how-large-the-terminal-number-can-be-in-a-for-loop/1030344/
// 
// This is my own implementation.
// I don't check the resulting squareroot, I check the square of c.
//

void setup() 
{
  Serial.begin(115200);
  Serial.println( "a    b    c");
}

void loop() 
{
  for( uint32_t a = 1; a<65535; a++)
  {
    for( uint32_t b = 1; b<65535; b++)
    {
      // temporary calculation
      uint32_t t = (a*a) + (b*b);   // bug ! this will not fit

      // get the integer squareroot
      uint32_t c = sqrt32( t);

      // check if it was a good number
      if( (c*c) == t)
      {
        Serial.print( a);
        Serial.print( ", ");
        Serial.print( b);
        Serial.print( ", ");
        Serial.print( c);
        Serial.println();
      }
    }
  }
}

// Integer squareroot, Newton methode.
// https://en.wikipedia.org/wiki/Integer_square_root
//
// Square root of integer
uint32_t sqrt32( uint32_t s)
{
  uint32_t x0 = s / 2;			// Initial estimate
	                          // Avoid overflow when s is the maximum representable value

  // Sanity check
  if( x0 != 0)
  {
    uint32_t x1 = (x0 + s / x0) / 2;	// Update

    while(x1 < x0)				// This also checks for cycle
    {
      x0 = x1;
      x1 = (x0 + s / x0) / 2;
    }

    return x0;
  }
  else
  {
    return s;
  }
}