is a perfect square.
on the 
-
.
the distance between 
and the line 
.
.
in terms of 
.
moves in the range of 
,
.
,
such that the inequality :![\[f(x) \leq f(x)^3-2f(x)^2+2\]](http://latex.artofproblemsolving.com/1/2/c/12c4c4c850c1c2886f002dfcb0bead075e2ab679.png)
.
Y by tenplusten, Tawan, Adventure10, Mango247
Let 
and 
be fixed distinct positive integers. A wren is on an infinite board indexed by 
, and from a square 
may move to any of the eight squares 
or 
. For each 
, determine the smallest number 
of moves required to travel from 
to 
, or prove that no such exists.
Proposed by Michael Ren
and 
be fixed distinct positive integers. A wren is on an infinite board indexed by 
, and from a square 
may move to any of the eight squares 
or 
. For each 
, determine the smallest number 
of moves required to travel from 
to 
, or prove that no such exists.Proposed by Michael Ren
or 
are both odd then no such 
and one of them, say 
where 
is defined as the least 
such that 
and 
is defined as either 
or 
,
there is no such 
and type 2 : 
.
iff 
,
type 1 moves. The same holds true for type 2 moves too.![$$(0,0) \xrightarrow[\text{type 1 only}]\ (am,bn) \xrightarrow[\text{type 2 only}]\ (am+cn,bn+dm) = (1,0)$$](http://latex.artofproblemsolving.com/2/2/4/22428b4b62ac21fb87e9256d3fba678d9ca25d2a.png)
Since 
,
and 
,
must be even. Thus 
is even too. Write 
.
.
of this will lead to a series of 
moves.
,
