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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.
 Winter '08
 ANDREWCHILDS
 Math, Congruence, Counting

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