#include <stdio.h>
#include <stdlib.h>
#include <time.h>

int const size = 20;

int main(void) {
  srand((unsigned)time(NULL));

  int rand_nums[size];

  for (int i = 0; i < size; ++i)
    rand_nums[i] = rand() % 10;

  for (int i = 0; i < size; ++i)
    printf("%d ", rand_nums[i]);
  puts("");
  
  int n_unique = 0;
  for (int i = 0; i < size; ++i) {
    for (int j = 0; j < n_unique; ++j) {
      if (rand_nums[i] == rand_nums[j])
	goto NOT_UNIQUE;
    }
    rand_nums[n_unique++] = rand_nums[i];
  NOT_UNIQUE:;
  }
  
  for (int i = 0; i < n_unique; ++i)
    printf("%d ", rand_nums[i]);
  puts("");
  
  return 0;
}

If you are OK with destroying the original array, you can even do this in place.

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

int const size = 20;

int main(void) {
  srand((unsigned)time(NULL));

  int rand_nums[size];

  for (int i = 0; i < size; ++i)
    rand_nums[i] = rand() % 10;

  for (int i = 0; i < size; ++i)
    printf("%d ", rand_nums[i]);
  puts("");
  
  int n_unique = 0;
  for (int i = 0; i < size; ++i) {
    for (int j = 0; j < n_unique; ++j) {
      if (rand_nums[i] == rand_nums[j])
	goto NOT_UNIQUE;
    }
    rand_nums[n_unique++] = rand_nums[i];
  NOT_UNIQUE:;
  }
  
  for (int i = 0; i < n_unique; ++i)
    printf("%d ", rand_nums[i]);
  puts("");
  
  return 0;
}

I won't apologize for the GOTO.

Clever!

I understood that @op had a hard requirement of using C, so even though int const size = 20; was the right thing to do in C++, I went for #define. This exercise showed me my C has become rusty, and C++ has spoiled me...

I understood that @op had a hard requirement of using C, so even though int const size = 20; was the right thing to do in C++, I went for #define. This exercise showed me my C has become rusty, and C++ has spoiled me...