Understanding the Problem
When a positive integer n is divided by 5 and yields a remainder of 3, it can be expressed mathematically as:
- n = 5k + 3, where k is a non-negative integer.
This means that n can take several values, such as 3, 8, 13, 18, etc., depending on the value of k.
Finding the Appropriate Number
To find a number that gives a remainder of 0 when divided by 5, we need to adjust n slightly. This can be done by finding a number that is greater than n and is a multiple of 5.
Calculating the Next Multiple of 5
To find the next integer multiple of 5 after n:
- The next multiple of 5 can be calculated by adding the difference needed to reach the next multiple.
- Since n = 5k + 3, the next multiple of 5 will be:
- 5(k + 1) = 5k + 5.
Now we can deduce:
- Next number = (5k + 3) + (5 - 3) = 5k + 5.
Conclusion
Thus, the number that yields a remainder of 0 when divided by 5 is:
- n + 2.
By adding 2 to n (which leaves a remainder of 3), you will arrive at the next multiple of 5, confirming that this number will yield a remainder of 0 when divided by 5.
For example, if n = 3, then n + 2 = 5, which is divisible by 5. If n = 8, then n + 2 = 10, and so on.
In summary, the required number is always n + 2, where n is your initial integer.