The Collatz Problem

# The Collatz Problem - Math 100 The Collatz Problem Martin H...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 100 The Collatz Problem Martin H. Weissman 1. Warm-up Problems Try the following problems for “warm-up”. Fill in the blanks in order to make true sentences. There can be more than one correct answer to each problem. Try to find multiple answers, when possible. (1) If x ≡ 3 (mod 5), then x 2 ≡ (mod 5)? (2) If x ≡ 1 (mod 4), then 3 x + 1 is divisible by ? (3) If x is divisible by 8, then x ≡ (mod 4)? (4) If x ≡ 1 (mod 8), then 3 x + 1 ≡ (mod 8)? (5) If x ≡ 5 (mod 16), then 3 x + 1 is divisible by ? (6) If x ≡ 3 (mod 8), then x ≡ (mod 4)? (7) If x ≡ 7 (mod 27), then x ≡ (mod 3)? (8) If x ≡ 1 (mod 4), then x ≡ (mod 8) or x ≡ (mod 8). 2. The Collatz “Game” The Collatz Game (or 3 n + 1 game) has the following rules: (1) Choose a positive integer n . (2) If n is odd, the next number is 3 n + 1. (3) If n is even, the next number is n/ 2. (4) Go back to Step 2, and repeat....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

The Collatz Problem - Math 100 The Collatz Problem Martin H...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online