Boil the diced potatoes in salted water until tender, about 15 minutes.
Drain and allow the potatoes to cool slightly.
Mash the potatoes in a large bowl until smooth.
Add the egg and salt, and mix well.
Gradually add flour until a dough forms.
Knead the dough gently on a floured surface until smooth.
Roll out the dough to about 1/4 inch thickness.
Cut the dough into thin strips to form noodles.
Boil a pot of salted water and add the noodles.
Cook for 3-4 minutes until they float, then drain and serve.