Let denote the number of partitions into parts not congruent to 0, , or (mod ). Let denote the number of partitions of wherein
1. 1 appears as a part at most times.
2. The total number of appearances of and (i.e., any two consecutive integers) together is at most .
Then Gordon's partition theorem states that for ,
The first Rogers-Ramanujan identity corresponds to , and the second to , .