Unformatted text preview: 1=0, 14+64+1 = 0. Prove that the alternating sum of the elements in the nth row of Pascal’s triangle is equal to 0, i.e. p n Pp n 1 P + p n 2 P ··· ± p n n P = 0 . 4. (a) (10 points) ±ind the greatest common denominator d of 731 and 645. (b) (10 points) Express d in the form 731 j + 645 k , with j and k integers. (c) (10 points) Give prime factorizations for 81 , 82 , 83. 5. (a) (10 points) Calculate the multiplicative inverse of 19 modulo 21. (b) (10 points) Explain why 14 does not have a multiplicative inverse modulo 21. END O± EXAMINATION 1...
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 Summer '08
 BESCHER
 Algebra, Prime number, Rational number, Greatest common divisor, multiplicative inverse modulo, greatest common denominator

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