To find the first day of the previous and following months relative to a given date, n would be -1 and 1:
mysql>
mysql> CREATE TABLE date_val
-> (
-> d DATE
-> );
Query OK, 0 rows affected (0.01 sec)
mysql>
mysql> INSERT INTO date_val (d) VALUES('1864-02-28');
Query OK, 1 row affected (0.00 sec)
mysql> INSERT INTO date_val (d) VALUES('1900-01-15');
Query OK, 1 row affected (0.00 sec)
mysql> INSERT INTO date_val (d) VALUES('1987-03-05');
Query OK, 1 row affected (0.00 sec)
mysql> INSERT INTO date_val (d) VALUES('1999-12-31');
Query OK, 1 row affected (0.00 sec)
mysql> INSERT INTO date_val (d) VALUES('2000-06-04');
Query OK, 1 row affected (0.00 sec)
mysql>
mysql>
mysql> SELECT d,
-> DATE_ADD(DATE_SUB(d,INTERVAL DAYOFMONTH(d)-1 DAY),INTERVAL -1 MONTH)
-> AS '1st of previous month',
-> DATE_ADD(DATE_SUB(d,INTERVAL DAYOFMONTH(d)-1 DAY),INTERVAL 1 MONTH)
-> AS '1st of following month'
-> FROM date_val;
+------------+-----------------------+------------------------+
| d | 1st of previous month | 1st of following month |
+------------+-----------------------+------------------------+
| 1864-02-28 | 1864-01-01 | 1864-03-01 |
| 1900-01-15 | 1899-12-01 | 1900-02-01 |
| 1987-03-05 | 1987-02-01 | 1987-04-01 |
| 1999-12-31 | 1999-11-01 | 2000-01-01 |
| 2000-06-04 | 2000-05-01 | 2000-07-01 |
+------------+-----------------------+------------------------+
5 rows in set (0.00 sec)
mysql>
mysql> drop table date_val;
Query OK, 0 rows affected (0.00 sec)
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