Let a be an integer and d be a positive integer. Show that the integers q and r with and which were shown to exist in Example 5, are unique.
The integers r and Q are unique.
The given data can be listed below as:
The integer is described as the whole number which does not provide a fractional value. The integer also does not have a fractional component.
Let the equation of the integer a can be expressed as:
Here, a is the value of the first integer and d is the value of the positive integer.
Here, and then the above equation can be expressed as:
It has been assumed that without the loss of the generality. Moreover, and hence is not divisible by d.
Now, if the above equation gets equal to zero, then and becomes a contradiction. Hence, r and Q are described as distinct.
Thus, the integers r and Q are unique.
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