## Compfiles: Catalog Of Math Problems Formalized In Lean

## Imo1978P1

```
import Mathlib.Tactic
/-!
# International Mathematical Olympiad 1978, Problem 1
m and n are positive integers with m < n.
The last three decimal digits of 1978m are the same as the last three decimal digits of 1978n.
Find m and n such that m + n has the least possible value.
-/
namespace Imo1978P1
/- determine -/ abbrev solution : ℕ × ℕ := sorry
theorem imo1978_p1 (m n : ℕ)
(hmn: m < n)
(hmn2: (m, n) = solution) :
(1978^m) % 1000 = (1978^n) % 1000 ∧
(∀ m' n' : ℕ, m' < n' ∧ (1978^m') % 1000 = (1978^n') % 1000 → m + n ≤ m' + n') := sorry
end Imo1978P1
```

File author(s): InternLM-MATH LEAN Formalizer v0.1

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