int gcd(int a, int b); An example run of your program is as follows: Enter the number to start searching for k (> 2, inclusive): 1 Enter the number to start searching for k (> 2, inclusive): 2 Enter the number to start searching for k (> 2, inclusive): 3 Enter the number to stop searching for k (inclusive): 2 Enter the number to stop searching for k (inclusive): 1 Enter the number to stop searching for k (inclusive): 20 Enter the number to start searching for a (> 0, inclusive): 0 Enter the number to start searching for a (> 0, inclusive): 1 Enter the number to stop searching for a (inclusive): 10000 Trying k = 3... Trying k = 4... Trying k = 5... Trying k = 6... Trying k = 7... Trying k = 8... Trying k = 9... Trying k = 10... Trying k = 11... Trying k = 12... Trying k = 13... Trying k = 14... Trying k = 15... Trying k = 16... Erdos-Woods number: 16 a = 2184
int gcd(int a, int b); An example run of your program is as follows: Enter the number to start searching for k (> 2, inclusive): 1 Enter the number to start searching for k (> 2, inclusive): 2 Enter the number to start searching for k (> 2, inclusive): 3 Enter the number to stop searching for k (inclusive): 2 Enter the number to stop searching for k (inclusive): 1 Enter the number to stop searching for k (inclusive): 20 Enter the number to start searching for a (> 0, inclusive): 0 Enter the number to start searching for a (> 0, inclusive): 1 Enter the number to stop searching for a (inclusive): 10000 Trying k = 3... Trying k = 4... Trying k = 5... Trying k = 6... Trying k = 7... Trying k = 8... Trying k = 9... Trying k = 10... Trying k = 11... Trying k = 12... Trying k = 13... Trying k = 14... Trying k = 15... Trying k = 16... Erdos-Woods number: 16 a = 2184
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int gcd(int a, int b);
An example run of your program is as follows:
Enter the number to start searching for k (> 2, inclusive): 1
Enter the number to start searching for k (> 2, inclusive): 2
Enter the number to start searching for k (> 2, inclusive): 3
Enter the number to stop searching for k (inclusive): 2
Enter the number to stop searching for k (inclusive): 1
Enter the number to stop searching for k (inclusive): 20
Enter the number to start searching for a (> 0, inclusive): 0
Enter the number to start searching for a (> 0, inclusive): 1
Enter the number to stop searching for a (inclusive): 10000
Trying k = 3...
Trying k = 4...
Trying k = 5...
Trying k = 6...
An example run of your program is as follows:
Enter the number to start searching for k (> 2, inclusive): 1
Enter the number to start searching for k (> 2, inclusive): 2
Enter the number to start searching for k (> 2, inclusive): 3
Enter the number to stop searching for k (inclusive): 2
Enter the number to stop searching for k (inclusive): 1
Enter the number to stop searching for k (inclusive): 20
Enter the number to start searching for a (> 0, inclusive): 0
Enter the number to start searching for a (> 0, inclusive): 1
Enter the number to stop searching for a (inclusive): 10000
Trying k = 3...
Trying k = 4...
Trying k = 5...
Trying k = 6...
Trying k = 7...
Trying k = 8...
Trying k = 9...
Trying k = 10...
Trying k = 11...
Trying k = 12...
Trying k = 13...
Trying k = 14...
Trying k = 15...
Trying k = 16...
Erdos-Woods number: 16
a = 2184
Trying k = 8...
Trying k = 9...
Trying k = 10...
Trying k = 11...
Trying k = 12...
Trying k = 13...
Trying k = 14...
Trying k = 15...
Trying k = 16...
Erdos-Woods number: 16
a = 2184
Transcribed Image Text:Expected
Enter the number to start searching for k (> 2,
inclusive): Enter the number to stop searching for k
(inclusive): Enter the number to start searching for
a (> 0, inclusive): Enter the number to stop
searching for a (inclusive): Trying k
Trying k = 20...
= 19...
Trying k
= 21...
Trying k = 22...
Erdos-Woods number: 22
a = 3521210
Transcribed Image Text:Part 2– Erdős-Woods Numbers
In this part, you are asked to write a complete C program that finds an Erdős-Woods number.
In number theory, a positive integer k is said to be an Erdős-Woods number if there exists a positive
integer a such that each of the consecutive integers a + i for 0 < i < k shares at least one prime
factor with either a or a + k. In other words, if for a k there is an a such that each evaluation of
ged(a, a + i) > 1 or gcd(a + k,a + i) >1 returns true, then k is an Erdős–Woods number.
For example, one a for k = 16 is 2184. 2184 is 2° x 3 x 7 × 13, while 2184 + 16 = 2200 =
28 x 52 x 11. We can easily verify that all the integers between 2185 and 2199 share at least a prime
factor with either 2184 or 2200.
Your C program should begin by prompting the user to enter four integers:
- The number to start searching for k. It needs to be greater than 2. Your program will start
searching for Erdős-Woods number from this starting point (inclusive).
- The number to stop searching for k (inclusive). It needs to be greater than the starting point
above searching for k.
- The number to start searching for a (inclusive). It needs to be positive (greater than 0).
- The number to stop searching for a (inclusive). It needs to be greater than the starting point
above searching for a.
When the stated requirements for these integers are not satisfied (for example, the starting point
searching for k is not greater than 2), the user will be repeatedly prompted to enter new values for
the same integer until the requirements are satisfied.
Once valid values for these four integers have been entered, your program should start from the
starting point of searching for k, and use the definition of Erdős–Woods number to see if k is an
Erdős-Woods number. To save some computation time, your program only needs to search in the
range specified by the user for a.
Your C program needs to define and use at least one function that computes the greatest common
divisor between two integers, a and b:
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