Large arrays, malloc, and strcmp

I have two fairly large 2d arrays to hold strings, and I want to compare each string in the second array to every string in the first to see if any match. The following is how I create the arrays, and how I compare them. It works if x(which is unsigned long b/c max number can be 4000000000) is a small number, but when it is a large number( 500000+ ), the programs seg faults at strcmp. Any ideas?

Code:

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unsigned long int x;
int y;

printf( "Enter the number of random words to be produced: " );
        scanf( "%u", &x );

printf( "Enter the maximum length of each word: " );
        scanf( "%d", &y);

char **buffer;
        buffer = malloc( x * sizeof(char *) + 1);
        for( i=0; i<x; i++) {
                buffer[i] = malloc( y * sizeof(char) + 1 );
        }

// Generate random words and store in a 2d buffer array.
// rand()%25 ensures only letters are generated.
   
        for( i=0; i<x; i++ ) {
                for( j=0; j<y-1; j++ ) {
                       
                        r = rand()%25;
                        buffer[i][j] = letters[r];
                       
                }
                // Ensure each string is null-terminated.
                buffer[i][j] = '\0';
        }

FILE *dict;
                dict = fopen( "linux.words", "r" );
               
        if( ! dict ) {
                printf( "Error: Failed to open linux.words\n" );
        }
       
               
        char dict_words[SIZE][WORD_SIZE], *z;
        i = 0;
        while( fgets( dict_words[i], 256, dict ) != NULL ) {
               
                i++;
        }
       
        // Remove newline character from each word to avoid comparison errors later.
        int p, len;
        for( p=0; p<i; p++ ) {
                if(( z = strchr( dict_words[p], '\n' ) )) *z = 0;
        }
       
        // Ensures all words in linux.words start with lower case letter.
        for( p=0; p<i; p++ ) {
                dict_words[p][0] = tolower( dict_words[p][0] );
        }


        }
        int k;
        for( j=0; j<i; j++ ) {
                for( k=0; k<x; k++ ) {
                        if( strcmp( dict_words[j], buffer[k] ) == 0 ) {
                                fputs( buffer[k], words_out);
                                fputs( "\n", words_out);
                               
                        }
                }
        }

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You're not checking the return value of your malloc()'s for NULL, plus you didn't say how big y is (the total amount of memory you're allocating is roughly x*y*sizeof(char *)).

Edit: Never mind my second comment, I overlooked the part about strcmp().

Edit: Your code is not self-contained - for example, the values of SIZE and WORD_SIZE, whatever they are, must be large enough. You also haven't given the definition of letters[].