login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A240129 Triangular numbers that are squares of triangular numbers. 1
0, 1, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Ljunggren used p-adic methods to prove that 0, 1, and 36 are the only triangular numbers that are squares of triangular numbers.
Same as: the only positive integer solutions of (x(x-1))^2 = 2y(y-1) are (x,y) = (1,1), (2,2), and (4,9).
Cassels used elliptic curves to simplify Ljunggren's proof.
Subsequence of A001110 (triangular numbers that are squares).
LINKS
EXAMPLE
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2 = (1 + 2 + 3)^2.
CROSSREFS
Sequence in context: A107736 A261121 A139474 * A023929 A010113 A167264
KEYWORD
nonn,fini,full,bref
AUTHOR
Jonathan Sondow, Apr 02 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)