Place the potatoes in a pot of cold water. Add a pinch of salt and bring to a boil. Bring the heat down to medium-high heat and boil for 15-20 minutes until the potatoes are fully cooked.
In the meantime, place the cucumbers in a bowl and sprinkle the salt over top. Allow this to sit for 5 minutes for the salt to remove the excess water from the cucumber. Then drain the water from the bowl and squeeze the cucumbers dry with a paper towel.
Drain the water from the pot, and place the pot over low heat. Mash the potatoes with a potato masher or potato ricer until smooth, then remove from the heat. Add the egg yolks and continue mashing until fully combined.
Add the cucumber, corn and black pepper and combine well. Then add the mayonnaise and mix until fully combined.