74hw6 - x and y , must it be true that 2 x 2 y (mod n ) if...

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Homework Assignment 6 Due: Wednesday, November 22 1. Prove that any two consecutive Fibonacci numbers are relatively prime. 2. Find the smallest positive integer a for which the equation 1602 · x + 1170 · y = 10 6 + a has a solution in integers x and y . Also, find one such solution. Hint: what do you know about the set { 1602 x + 1170 y | x, y Z } ? 3. (a) For natural numbers
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Unformatted text preview: x and y , must it be true that 2 x 2 y (mod n ) if x y (mod n )? (b) Show that 2 70 + 3 70 is divisible by 13. (c) Calculate the last two digits of 3 1200 . 4. Suppose that n > 1 is a positive integer greater such that 2 n + n 2 is prime. Show that n is divisible by 3. (Hint: work in mod 6.)...
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