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Unformatted text preview: 6) Yes or No: Is 3709 â‰¡ 37 (mod 51) ? Justify your answer. (5 points) 7) Prove: If a â‰¡ b (mod m ) and c â‰¡ d (mod m ), then a + c â‰¡ b + d (mod m ). Assume that a , b , c , d , and m are integers, with m > 2. (10 points) 8) The binary representation of a positive integer is 1001001. What is the decimal representation of this integer? (5 points) 9) The decimal representation of a positive integer is 182. What is the binary representation of this integer? (5 points) 10) Use the method shown in class to find two integers s and t such that 1 = 59 s + 56 t . (10 points) 11) Use the method shown in class to find three positive integer solutions to the linear congruence 11 x + 4 â‰¡ 13 (mod 15). â€¢ Hint: 1 = (15)(3)  (11)(4). â€¢ A "bruteforce" approach will not receive full credit! (10 points)...
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 Spring '11
 staff
 Math, Number Theory, Natural number, Prime number, prime Factorization

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