Boil the potatoes with the skin on until cooked, then let them cool.
Peel the boiled potatoes and mash them.
Peel the boiled eggs.
Roughly chop the eggs and mix them with the potatoes.
Thinly slice the cucumber and carrot, then season with salt.
Combine the potatoes, eggs, cucumber, and carrot in a bowl, and season with mayonnaise, salt, and pepper.