math135-a8 - over, when they formed groups of 11 there were...

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Assignment 8 – Questions 1. Solve the following pairs of congruences. 15 x 4 (mod 26) 24 x 6 (mod 63) 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 5000 troops before a battle, and after the battle it was found that when the troops formed groups of 5 there was 1 left over, when they formed groups of 7 there were none left
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Unformatted text preview: over, when they formed groups of 11 there were 6 left over, and when they formed groups of 12 there were 5 left over. How many troops survived the battle? 3. Prove that 21 | (3 n 7 + 7 n 3 + 11 n ) for all integers n. 4. Find the last two digits of 279 669 . 5. If ( m ) is the Euler -function, prove that ( m ) = (2 m ) if and only if m is odd. 1...
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This note was uploaded on 07/24/2011 for the course MATH 135 taught by Professor Andrewchilds during the Winter '08 term at Waterloo.

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