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Unformatted text preview: b ( mod n ) 5. Prove that if the last digit of n is 3, then n is not a perfect square. 6. Give an example of integers a,k,l,m such that k l ( mod m ), but a k 6 a l ( mod m ) 7. (a) Find a solution to 5 x 1 ( mod 6). Your answer is called a multiplicative inverse of 5, mod 6 because it behaves similar to 1 5 . (b) Show that 2 has no multiplicative inverse mod 6. That is, show that 1 2 has no meaning when working mod 6. 8. Show that a natural number n is divisible by 11 i the alternating sum of its digits is too (ie, rst digit second + third  fourth + )...
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This note was uploaded on 08/31/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at University of California, Berkeley.
 Summer '08
 STRAIN
 Math

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