[/quote]
,
with the property that for every real numbers 
and 
it holds that
along the perimeter of a circle, then every word of the length 
consisting of letters 
and 
(i.e. 
,
,
,
,
,
,
,
)
-
(i.e. an ordered 
and 
.
be 
positive integers such that the 
products![\[a_1 a_2 a_3 \cdots a_n, b_1 a_2 a_3 \cdots a_n, b_1 b_2 a_3 \cdots a_n, \dots, b_1 b_2 b_3 \cdots b_n\]](http://latex.artofproblemsolving.com/0/2/c/02cbff15c4d0118156a9d24be09360facb264d5a.png)
form a strictly increasing arithmetic progression in that order. Determine the smallest possible integer that could be the common difference of such an arithmetic progression.
Prove that
Where 
Prove that
be complex numbers such that 
and 
.
be positive real numbers such that 
and 
,
is defined below. 
Show that for all nonnegative integer 
,
is a positive integer.
![\[\frac {x^{7} - 1}{x - 1} = y^{5} - 1.\]](http://latex.artofproblemsolving.com/7/6/2/762492979b016e0f573b993b67a2b26dfb8888f4.png)
be a prime such that: 
.
Prove that
Where 
Prove that
Let 
Prove that
Y by whwlqkd, cubres
Is it true that
?
A=1728400904217815186787639216753921417860004366580219212750904
024377969478249664644267971025952530803647043121025959018172048
336953969062151534282052863307398281681465366665810775710867856
720572225880311472925624694183944650261079955759251769111321319
421445397848518597584590900951222557860592579005088853698315463
815905425095325508106272375728975
B=2275643401548081847207782760491442295266487354750527085289354
965376765188468052271190172787064418854789322484305145310707614
546573398182642923893780527037224143380886260467760991228567577
953725945090125797351518670892779468968705801340068681556238850
340398780828104506916965606659768601942798676554332768254089685
307970609932846902
?A=1728400904217815186787639216753921417860004366580219212750904
024377969478249664644267971025952530803647043121025959018172048
336953969062151534282052863307398281681465366665810775710867856
720572225880311472925624694183944650261079955759251769111321319
421445397848518597584590900951222557860592579005088853698315463
815905425095325508106272375728975
B=2275643401548081847207782760491442295266487354750527085289354
965376765188468052271190172787064418854789322484305145310707614
546573398182642923893780527037224143380886260467760991228567577
953725945090125797351518670892779468968705801340068681556238850
340398780828104506916965606659768601942798676554332768254089685
307970609932846902
This post has been edited 6 times. Last edited by Dattier, Mar 16, 2025, 10:10 AM
.
