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MAT135-Assignment8

MAT135-Assignment8 - over when they formed groups of 7...

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MATH 135, Fall 2010 Assignment #8 Due at 4:00pm on Tuesday, November 16 Problem 1 . (a) Prove that 2 n 25 + 10 n 13 + 14 n 9 + 9 n 0 (mod 5) for all n Z . (b) Prove that 35 | 2 n 25 + 10 n 13 + 14 n 9 + 9 n for all n Z Problem 2 . Chinese generals used to count their troops by telling them to form groups of some size n , and then counting the number of troops left over. Suppose there were 10000 troops before a battle, and after the battle it was found that when the troops formed groups of 5 there was 1 left
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Unformatted text preview: over, when they formed groups of 7 there were 2 left over, when they formed groups of 11 there were 9 left over, and when they formed groups of 17 there were 3 left over. How many troops survived the battle? Problem 3 . Find 53 37 54 (mod 23). Problem 4 . Find the last two digits of 287 449 . 1...
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