Explanation Given information: There exist quotients and remainders but also that the quotient and remainder of a division are unique. Proof: To proof: q 1 = q 2 and r 1 = r 2 Suppose a and d are integers with d > 0 and that q 1 , r 1 , q 2 and r 2 are integers such that a = d q 1 + r 1 where 0 ≤ r 1 < d , and a = d q 2 + r 2 where 0 ≤ r 2 < d . Equating both equations, d q 1 + r 1 = d q 2 + r 2 r 2 − r 1 = d q 1 − d q 2 = d ( q 1 − q 2 ) ........... ( i ) Both r 1 and r 2 lies between 0 and d

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ISBN: 9780357540244

Author: EPP

Publisher: CENGAGE L

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Chapter 4.8, Problem 21ES

To determine

To prove:

If a and d are integers with d > 0 and q₁, r₁, q₂ and r₂ are integers such that

a=dq1+r1          where     0≤r1<d, and

a=dq2+r2          where     0≤r2<d, then

q1=q2       and        r1=r2.

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Chapter 4.8, Problem 20ES

Chapter 4.8, Problem 22ES

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Chapter 4 Solutions

WEBASSIGN F/EPPS DISCRETE MATHEMATICS

Ch. 4.1 - An integer is even if, and only if,_______.Ch. 4.1 - An integer is odd if, and only if,____Ch. 4.1 - An integer n is prime if, and only if,_______Ch. 4.1 - The most common way to disprove a universal...Ch. 4.1 - Prob. 5TY Ch. 4.1 - To use the method of direct proof to prove a...Ch. 4.1 - In 1-4 justify your answer by using the...Ch. 4.1 - In 1-4 justify your answer by using by the...Ch. 4.1 - In 1-4 justify your answers by using the...Ch. 4.1 - In 1-4 justify your answers by using the...

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To prove: If a and d are integers with d > 0 and q 1 , r 1 , q 2 and r 2 are integers such that a = d q 1 + r 1 where 0 ≤ r 1 < d , and a = d q 2 + r 2 where 0 ≤ r 2 < d , then q 1 = q 2 and r 1 = r 2 .

Solution Summary: The author explains that quotients and remainders of a division are unique.

Videos

To prove:

If a and d are integers with d > 0 and q₁, r₁, q₂ and r₂ are integers such that

a=dq1+r1          where     0≤r1<d, and

a=dq2+r2          where     0≤r2<d, then

q1=q2       and        r1=r2.

Want to see the full answer?

Chapter 4 Solutions

To prove: If a and d are integers with d &gt; 0 and q 1 , r 1 , q 2 and r 2 are integers such that a = d q 1 + r 1 where 0 ≤ r 1 &lt; d , and a = d q 2 + r 2 where 0 ≤ r 2 &lt; d , then q 1 = q 2 and r 1 = r 2 .

Solution Summary: The author explains that quotients and remainders of a division are unique.

Videos

To prove: If a and d are integers with d > 0 and q1, r1, q2 and r2 are integers such that a=dq1+r1 where 0≤r1<d, and a=dq2+r2 where 0≤r2<d, then q1=q2 and r1=r2.

Want to see the full answer?

Chapter 4 Solutions

To prove: If a and d are integers with d > 0 and q 1 , r 1 , q 2 and r 2 are integers such that a = d q 1 + r 1 where 0 ≤ r 1 < d , and a = d q 2 + r 2 where 0 ≤ r 2 < d , then q 1 = q 2 and r 1 = r 2 .

To prove:

If a and d are integers with d > 0 and q₁, r₁, q₂ and r₂ are integers such that

a=dq1+r1 where 0≤r1<d, and

a=dq2+r2 where 0≤r2<d, then

q1=q2 and r1=r2.