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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
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1/a+b+x =1/a+1/b+1/x a+b ≠ 0 Ans: 1/a+b+x =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒ x - ( a + b + x )/ x ( a + b + x ) = + a + b/ ab ⇒
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