,![\[
\frac{a}{b} + \frac{b}{c} + \frac{c}{a}.
\]](http://latex.artofproblemsolving.com/3/2/b/32b41635c159921e11245369e66185ec69b0d785.png)
,
be a scalene triangle. 
is the foot of the altitude from 
to 
.
is the orthocenter, 
is the midpoint of 
is the midpoint of 
.
and 
to the circumcircle of 
.
passes through one of the intersections of circles 
with 
.
are positiv real number, such that 
,
Y by Amir Hossein, astamir, bluecarneal, nsun48, rdj5933mile5, shinichiman, avatarofakato, Debdut, bryanbr2, airplanes1, dantx5, silly_mouse, Binomial-theorem, knittingfrenzy18, AdvitiyaBrijesh, ahaanomegas, forthegreatergood, bcp123, minimario, Mathematicalx, Nashimo, mikechen, Devesh14, trumpeter, ais3000, Magikarp1, Wave-Particle, eshan, m1234567, zed1969, JasperL, Wavefunction, rodamaral, mathleticguyyy, Toinfinity, Chipaoo, rg_ryse, Adventure10, Mango247, and 21 other users
As our initial entry of a series of featured articles, Amir Hossein Parvardi (Amir Hossein) has written "Lifting the Exponent Lemma (LTE)," which is a useful result for solving exponential Diophantine equations.
This post has been edited 2 times. Last edited by Amir Hossein, Oct 22, 2016, 6:45 AM
Reason: Edited the link (and my username).
Reason: Edited the link (and my username).
o
o
u
.
and 
the number 
is a positive integer. Show that 
where 
is the least common denominator of 
.
,
of 
for infinitely many 
and 
or 
(otherwise it would divide them both and we could reduce the fractions). Led 
be the least power such that 
.
for some integer 
(just not to consider 
separately). But 
grows only logarithmically in 
is the number which satisfies 
by myself. And I am posting my proof.
,
to 
,
,
.
.
.
