D. Latvia 2021 Problem 5

Find all integer pairs $(a, b)$ such that $$(19 a + b) ^ {18} + (a + b) ^ {18} + (a + 19 b) ^ {18}$$ is a perfect square.

import Mathlib.Algebra.Group.Int.Defs
import Mathlib.Data.Set.Defs

def answer : Set (ℤ × ℤ) := sorry

theorem solution (a b : ℤ) : (∃ c, c ^ 2 = (19 * a + b) ^ 18 + (a + b) ^ 18 + (a + 19 * b) ^ 18) ↔
    (a, b) ∈ answer := sorry

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