.
:o
so 
and since 
is just 
therefore 
so 
to 
have the digit 
and are divisible by 
?
Y by
A point 
and two lines 
and 
are given in the space. For each nonnegative integer 
we denote by 
the projection of 
on 
and by 
the projection of on 
Prove that there exist two segments ![$[A'A''] \subset d_1$](//latex.artofproblemsolving.com/8/8/6/88667ee717ddd630efd34a9c4c83ee359c4897ed.png)
and ![$[B'B''] \subset d_2$](//latex.artofproblemsolving.com/3/7/4/374927492266c8adaed5d34e3871d250baba9c1b.png)
of length 
and a nonnegative integer 
such that ![$A_n \in [A'A'']$](//latex.artofproblemsolving.com/4/8/5/4851110dd8f0bf0ee7e42239ee051da76f5fbd65.png)
and ![$B_n \in [B'B'']$](//latex.artofproblemsolving.com/5/e/7/5e7d78dd940f5c81673b779a9b45e83f4dc05b4d.png)
for any 
and two lines 
and 
are given in the space. For each nonnegative integer 
we denote by 
the projection of 
on 
and by 
the projection of on 
Prove that there exist two segments ![$[A'A''] \subset d_1$](http://latex.artofproblemsolving.com/8/8/6/88667ee717ddd630efd34a9c4c83ee359c4897ed.png)
and ![$[B'B''] \subset d_2$](http://latex.artofproblemsolving.com/3/7/4/374927492266c8adaed5d34e3871d250baba9c1b.png)
of length 
and a nonnegative integer 
such that ![$A_n \in [A'A'']$](http://latex.artofproblemsolving.com/4/8/5/4851110dd8f0bf0ee7e42239ee051da76f5fbd65.png)
and ![$B_n \in [B'B'']$](http://latex.artofproblemsolving.com/5/e/7/5e7d78dd940f5c81673b779a9b45e83f4dc05b4d.png)
for any 
This post has been edited 1 time. Last edited by Filipjack, Apr 6, 2025, 4:56 PM
