import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem mathd_algebra_289
  (k t m n : ℕ)
  (h₀ : Nat.Prime m ∧ Nat.Prime n)
  (h₁ : t < k)
  (h₂ : k^2 - m * k + n = 0)
  (h₃ : t^2 - m * t + n = 0) :
  m^n + n^m + k^t + t^k = 20 := by sorry