If p is a positive integer such that the reminder when 4p divided by 9...
Problem: Find a possible value of p if the reminder when 4p is divided by 9 is 5.
Solution:Step 1: Understanding the problem
We need to find a positive integer p such that when 4p is divided by 9, the remainder is 5.
Step 2: Using the concept of remainders
We know that if a number n is divided by d, then the remainder r is such that 0 <= r="">< d.="" />
In this case, we are given that the remainder when 4p is divided by 9 is 5.
This means that 4p can be written as 9q + 5, where q is some integer.
Simplifying this equation, we get:
4p = 9q + 5
=> 4p - 5 = 9q
Step 3: Finding a possible value of p
We need to find a positive integer p that satisfies the above equation.
We can use trial and error method to find a possible value of p.
Let's start by assuming q = 1.
=> 4p - 5 = 9
=> 4p = 14
=> p = 3.5
Since p has to be a positive integer, this value of p is not valid.
Let's try with q = 2.
=> 4p - 5 = 18
=> 4p = 23
=> p = 5.75
Again, this value of p is not valid as p has to be a positive integer.
Let's try with q = 3.
=> 4p - 5 = 27
=> 4p = 32
=> p = 8
This value of p satisfies the given condition as the remainder when 4p is divided by 9 is 5.
Step 4: Conclusion
Therefore, a possible value of p is 8.
Final Answer: 8.