homework1 - + f 2 n-1 4. Find the quotient and remainder in...

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THEORY OF NUMBERS, Math 115 A Homework 1 Due Wednesday October 3 1. Use the well-ordering property to show that 3 is irrational. 2. Find a formula for n k =1 k 3 . 3. Find and prove a simple formula for the sum of the first n Fibonacci numbers with odd indices when n is a positive integers, i.e. find a formula for f 1 + f 3 + . . .
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Unformatted text preview: + f 2 n-1 4. Find the quotient and remainder in the division algorithm, with divisor 17 and dividend a) 100, b) -44, c) 289 5. Show that if a is an integer, then 3 divides a 3-a . 6. Show that the n-th Fibonacci number f n is divisible by 4 if and only if n is divisible by 6. 1...
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This note was uploaded on 04/08/2008 for the course MATH 115A taught by Professor Santos during the Fall '07 term at UC Davis.

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