Euler's 
theorem states that every prime of
the form 
,
(i.e., 7, 13, 19, 31, 37, 43, 61, 67, ..., which are also the primes of the form
;
OEIS A002476) can be written in the form 
with 
and 
positive integers.
The first few positive integers that can be represented in this form (with 
) are 4, 7, 12, 13, 16, 19, ... (OEIS A092572),
summarized in the following table together with their representations.
 |  |
| 4 | (1, 1) |
| 7 | (2, 1) |
| 12 | (3, 1) |
| 13 | (1, 2) |
| 16 | (2, 2) |
| 19 | (4, 1) |
| 21 | (3, 2) |
| 28 | (1, 3), (4, 2), (5, 1) |
| 31 | (2, 3) |
Restricting solutions such that 
(i.e., 
and 
are relatively prime), the numbers that can be represented
as 
are 4, 7, 12, 13, 19, 21, 28, 31, 37, 39, 43, ... (OEIS A092574),
as summarized in the following table.
 |  with  |
| 4 | (1, 1) |
| 7 | (2, 1) |
| 12 | (3, 1) |
| 13 | (1, 2) |
| 19 | (4, 1) |
| 21 | (3, 2) |
| 28 | (1, 3), (5, 1) |
| 31 | (2, 3) |
| 37 | (5, 2) |
