# mt6 - 2010 when divided by 7 4 Using Euler’s Theorem...

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Homework 6, Math 245, Fall 2010 Due Wednesday, December 1 in class. The solution of each exercise should be at most one page long. If you can, try to write your solutions in LaTex. Each question is worth 2 points. 1. Find all integers x that satisfy the following equations: x 1 (mod 4) x 3 (mod 7) x 7 (mod 15) 2. Find all integers x that satisfy the following equations: 3 x 1 (mod 8) 5 x 4 (mod 9) 3. Using Fermat’s Little Theorem, determine the integer remainder of 3
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Unformatted text preview: 2010 when divided by 7. 4. Using Euler’s Theorem, ﬁnd the last two digits of the number 3 2010 in the decimal representation. 5. If n is any integer, prove that n 2 ≡ 0 (mod 4) or n 2 ≡ 1 (mod 8). 6. Bonus Question! Find the last three digits of 2 2010 in the decimal representation....
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## This note was uploaded on 12/07/2011 for the course MATH 245 taught by Professor Cioaba during the Fall '10 term at University of Delaware.

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