Assignment3

# Assignment3 - n 2 â‰ 1(mod 8 5 Compute using the Euclidean...

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Math 240, Fall 2009 — Assignment 3 — Due: Monday, October 19 1. Show that if f ( x ) is a polynomial of degree n with real coefficients, then f ( x ) is Ω( x n ). 2. Prove, using induction, that 1 3 + 2 3 + 3 3 + · · · + n 3 = n ( n + 1) 2 2 for all positive integers n . 3. Prove, using induction, that 1 2 n 1 · 3 · 5 · · · (2 n - 1) 2 · 4 · 6 · · · (2 n ) whenever n is a positive integer. 4. Prove that if n is an odd positive integer then

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Unformatted text preview: n 2 â‰¡ 1 (mod 8). 5. Compute using the Euclidean algorithm: (a) GCD(1529, 14039) (b) GCD(1529, 14038) (c) GCD(1111111, 11111111) 6. Compute 10 785 (mod 23). Math 240 â€” Assignment 3 â€” Fall 2009 Marker: Gabriel Charette Instructor: Benjamin Young Date: Name: Student Number:...
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