Intended for: December 1, 2011
Timetable
- First draft entered by Alonso del Arte on August 28, 2011 ✓
- Draft reviewed by Daniel Forgues on December 1, 2011 ✓
- Draft to be approved by November 1, 2011
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A188892: Numbers
such that there is no triangular
-gonal number greater than
1.
-
{ 11, 18, 38, 102, 198, 326, 486, ... }
The
triangular numbers are essentially the building blocks of the other
figurate numbers. Therefore it is rather surprising that there can be sequences of
-gonal numbers that don’t overlap with the sequence of triangular numbers at all (other than
0 and
1).
T. D. Noe has demonstrated that the equation
| x 2 + x = (n − 2) y 2 − (n − 4) y |
has no integer solutions
, as conversion to a
generalized Pell equation shows that if
, then the first equation has only a finite number of solutions. From there one can pinpoint those values of
that produce no integer solutions greater than
1.
