Latvian National 2025 Grade 10 Problem 1

Do there exist integers $a, b, c, d$ such that
$$|a - b| + |b - c| + |c - d| + |d - a| = 2025?$$

Replace sorry in the template below with your solution. See Answer Bank for acceptible answer declarations. Mathlib version used by the checker is v4.34.0.

import Mathlib.Algebra.Group.Int.Defs
import Mathlib.Algebra.Order.Group.Unbundled.Abs

def answer : Prop := sorry

theorem solution : (∃ a b c d : ℤ, |a - b| + |b - c| + |c - d| + |d - a| = 2025) ↔ answer := sorry

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