import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Data.Nat.Prime
import Mathlib.Algebra.Associated
import Mathlib.Data.Int.Basic
import Mathlib.Tactic.Ring

/-!
# Hungarian Mathematical Olympiad 1998, Problem 6

Let x, y, z be integers with z > 1. Show that

 (x + 1)² + (x + 2)² + ... + (x + 99)² ≠ yᶻ.
-/

namespace Hungary1998P6
open BigOperators

theorem hungary1998_p6 (x y : ℤ) (z : ℕ) (hz : 1 < z) :
    ∑ i in Finset.range 99, (x + i + 1)^2 ≠ y^z := sorry

This problem has a complete solution written by David Renshaw.