Unformatted text preview: multiples of 5. 6. Find the least positive residues (that is, the remainders) modulo 47 of each of the following integers: a) 2 32 , b) 2 47 , c) 2 200 , 7. Let a = 4444 4444 . Let b be the sum of the digits of a , when written in decimal. Let c be the sum of the digits of b , when written in decimal. Find the sum of the digits of c . 8. Find all solutions of the following linear congruences: a) 17 x 14 (mod 21), b) 128 x 833 (mod 1001), c) 987 x 610 (mod 1597). 9. For which integers c , 0 c 30, does the congruence 12 x c (mod 30) have solutions? When there are solutions, how many incongruent ones are there? 10. Determine which integers a , where 1 a 14, have an inverse modulo 14. Find the inverse of each. 1...
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 Fall '07
 Santos
 Number Theory, Fractions, Remainder, Natural number, Prime number, Franc

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