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 
, 
.
