Boil the potatoes with the skin on until cooked, then peel them.
Mash the potatoes and let them cool.
Thinly slice the cucumber and carrot, salt them, then remove excess moisture.
Finely chop the boiled egg.
Combine the mashed potatoes, cucumber, carrot, egg, mayonnaise, salt, and pepper. Mix well.
Serve the finished salad in a bowl.