The Collatz Problem

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

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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....
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This note was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at UCSC.

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

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