Answer:
The programming language is not stated;
I'll answer this question using python programming language
The program starts here (Lines written in bold are comments and are used for explanatory purpose)
#This line imports the random module into the program
import random
#This line prompts the user to enter the filename
filename = input("Enter file name: ")
#This line prompts the user to enter the number of random numbers to generate
num = int(input("Number of random numbers: "))
#This line adjusts the filename to a .txt file
filename = filename+".txt"
#This line checks if the filename exists; if yes, it creates and open a new file and if otherwise, it uses the existing filr
f = open(filename,'a+')
#This line iterates through the number of random to generate
for i in range(1,num+1):
#This line generates random number within the range of 1 to 1000
n = random.randint(1,1000)
#This line prints the generated random number to file
print(n, file = f)
#This line closes the created file
f.close()