@article {MATHEDUC.05800663,
author = {Breu, Raymund and van der Poorten, Alf},
title = {Self-similar values of quadratic forms: A remark on pattern and duality.},
year = {2010},
journal = {Journal of Recreational Mathematics},
volume = {35},
number = {3},
issn = {0022-412X},
pages = {202-212},
publisher = {Baywood Publishing Company, Amityville, NY},
abstract = {Summary: Our text is Hendrik Lenstra's nice observation that $12^2+33^2=1233$. One notices readily that such a cute decomposition of $10^ka+b$ as a sum of two squares $a^2+b^2$ is no more than rewriting the sum of squares $10^{2k}+1$ as a different sum $(10^k-2a)^2+(2b-1)$. But that does not hint at more radical generalization. We show here that much the same can be told with the sum of squares $x^2+y^2$ replaced by an arbitrary quadratic form $f(x,y)=ux^2+ vxy+wy^2$, where $u,v$, and $w$ are integers; and the cute representations now are of the shape $10^ka+b=f(a,b)$.},
msc2010 = {F60xx},
identifier = {2010e.00418},
}