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Unformatted text preview: 1 Problem 5. Find the smallest positive integer with the property that, if you move the ±rst digit to the end, the new number is 1.5 times larger than the old one. Problem 6. Two players A and B alternatively take chips from two piles with a and b chips, respectively. Initially a > b . A move consists of taking from a pile a multiple of the other pile. The winner is the one who takes the last chip in one of the piles. Show that if a > 2 b , then the ±rst player A can force a win. Problem 7. Prove that n ( n + 1) divides 2(1 k + 2 k + · · · + n k ) for odd k . 2...
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 Spring '11
 Dolatabadi
 Prime number, positive integers, positive integer, Discrete Mathematics Homework

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