Unformatted text preview: k | m . Prove that a ‚Č° b (mod k ). 7. Suppose gcd( a, 21) = 1. Use Fermat‚Äôs Theorem to prove that a 6 ‚Č° 1 (mod 21). 8. A drawer contains 7 red socks, 10 white socks and 8 blue socks. You grab three of the socks at random. What is the probability that all three are the same color? 9. Let S be a square of side length 1. Let P 1 , . . . , P 101 be 101 points inside of S . Prove that two of the points are a distance ‚Č§ ‚ąö 2 / 10 apart. Hint: partition S into little squares of side 1 10 , and use the pigeonhole principle....
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This note was uploaded on 01/27/2010 for the course MATH 347 taught by Professor ? during the Spring '09 term at University of Illinois at Urbana‚ÄďChampaign.
- Spring '09