Update Fri Sep 27 01:40:51 EDT 2024

Math2001/Homework/hw4.lean

@@ -0,0 +1,46 @@
+/- Copyright (c) Heather Macbeth, 2023.  All rights reserved. -/
+import Library.Basic
+import Library.Theory.ModEq.Defs
+import AutograderLib
+
+math2001_init
+
+open Int
+
+/-! # Homework 4
+
+Don't forget to compare with the text version,
+https://github.com/hrmacbeth/math2001/wiki/Homework-4,
+for clearer statements and any special instructions. -/
+
+@[autograded 5]
+theorem problem1 (n : ℤ) : Odd (3 * n ^ 2 + 3 * n - 1) := by
+  sorry
+
+@[autograded 1]
+theorem problem2 : (8 : ℤ) ∣ 96 := by
+  sorry
+
+@[autograded 2]
+theorem problem3 : ¬(8 : ℤ) ∣ -55 := by
+  sorry
+
+@[autograded 4]
+theorem problem4 {a b c : ℤ} (hab : a ^ 3 ∣ b) (hbc : b ^ 2 ∣ c) : a ^ 6 ∣ c := by
+  sorry
+
+@[autograded 1]
+theorem problem5 : 31 ≡ 13 [ZMOD 3] := by
+  sorry
+
+@[autograded 2]
+theorem problem6 : ¬ 51 ≡ 62 [ZMOD 5] := by
+  sorry
+
+@[autograded 5]
+theorem problem7 (h : a ≡ b [ZMOD n]) : a ^ 3 ≡ b ^ 3 [ZMOD n] := by
+  sorry
+
+@[autograded 5]
+theorem problem8 (h1 : a ≡ b [ZMOD n]) (h2 : b ≡ c [ZMOD n]) : a ≡ c [ZMOD n] := by
+  sorry