Find the integer a such thata) a 43 (mod 23) and -22 a

Chapter 4, Problem 24E

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QUESTION:

Find the integer a such thata) a ? 43 (mod 23) and -22 ? a ? 0.________________b) a ? 17 (mod 29) and -14 ? a ? 14.________________c) a ? -11 (mod 21) and 90 ? a ? 110.

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QUESTION:

Find the integer a such thata) a ? 43 (mod 23) and -22 ? a ? 0.________________b) a ? 17 (mod 29) and -14 ? a ? 14.________________c) a ? -11 (mod 21) and 90 ? a ? 110.

ANSWER:

Solution:Step 1Here, in these problems we have to find integer a such that a b (mod m). a b (mod m) means integer a is congruent to b (mod m) and we can say integer a is congruent to b (mod) m, if a and b are integers and m is a positive integer and m divides( a-b) completely.Or,We can also say a is congruent to b (mod) m. if value of .To find integer congruent to b (mod) m, we have to find integer a such that (a-b) is divisible by m.In mathematical equation we can say =k. Where, k is an integer.

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