Place the potatoes into a pot and cover with salted water. Bring to the boil over high heat, then reduce heat to medium-low, cover and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two. Allow the potatoes to cool.
While the potatoes are cooking, place the eggs into a saucepan in a single layer and fill with water to cover the eggs by 2.5cm. Cover the saucepan and bring the water to the boil over high heat. Once the water is boiling, remove from the heat and let the eggs stand in the hot water for 15 minutes. Pour out the hot water, then cool the eggs under cold running water in the sink. Peel and dice once cold.
Place the potatoes, beetroots, eggs and mayonnaise into a bowl, mix well and season to taste with salt and pepper.