How do I make sure every character in a string argv[1] is digit in C?

I was doing an encryption exercise in CS50, and I got stuck There is this part: "Add to caesar.c, below main, a function called, e.g., only_digits that takes a string as an argument and returns true if that string contains only digits, 0 through 9, else it returns false. Be sure to add the function’s prototype above main as well".

And here's my code:

#include <cs50.h>
#include <stdio.h>
#include <ctype.h>
#include <string.h>

bool only_digits(string s);

int main(int argc, string argv[])
{
    // Make sure program was run with just one command-line argument

    argc = only_digits(argv[1]);
    if(argc != 2)
    {
        printf("Usage: ./caesar key\n");
        return 1;
    }
    return 0;

}

// make sure that the character in argv[1] is a digit

bool only_digits(string s)
{
    // int n = strlen(s);
    for (int i = 0, n = strlen(s); i < n; i++)
    {
        if(isdigit(s[i]))
        {
            return 0;
        }
    }
    printf("Usage: ./caesar key\n");
    return 1;
}

I decided to make a for loop, where I could check whether the characters are digits, but I need only to check the second character, not "caesar", and because of that, I presume, my code fails and comes with "Usage: ./caesar key\n" all the time, and if I write only "./caesar" - it comes with "Segmentation fault (core dumped)". Apparently my code is flawed, but I can't find the solution to it.

Solution

Let's note a few mistakes/misuse.

You can do this but I discourage you to.. Leave the argc aside. I mean, do not reuse it for something else. Create a dedicated variable instead..
Always check for validity of input argument(s) before processing them. In your case, when the user gives no input you still check for number. The makes you access invalid memory area and can trigger a segmentation fault.
In the example code you provide, only_digits either returns 0 or 1. Thus, checking if(argc != 2) always gets satisfied.
Your function only_digits is supposed to return a boolean => either true (or 1) or false (or 0). By convention, during your learning process, I advice you to stick to true and false.
Your function only_digits has a negated logic. It will return true if it has non digit only.

The resulting code would look like this:

#include <stdio.h>
#include <ctype.h>
#include <string.h>

bool only_digits(string s);

int main(int argc, string argv[])
{
    /* Make sure there are enough arguments passed to your program. */
    if (argc < 2) {
        goto usage;
    }

    // Make sure program was run with just one command-line argument
    bool isvalid = only_digits(argv[1]);
    if(isvalid == 0) {
        goto usage;
    }

    // everything is good.
    return 0;

usage:
    printf("Usage: ./caesar key\n");
    return 1;
}

// make sure that the character in argv[1] is a digit

bool only_digits(string s)
{
    for (int i = 0; i < strlen(s); i++) {
        /* Here, we want to break the loop upon the first non-digit
         * character. Thus the negation `!` */
        if(!isdigit(s[i])) {
            return false;
        }
    }

    return true;
}