[/quote]
,
be an even prime number and a sequence 
satisfy 
and 
Prove that always exists positive integer 
satisfying for all positive integers 
,
.
is "not congruence"
be pairwise coprime positive integers with 
being prime and 
.![$I = [0, a_1 a_2 \cdots a_n ]$](http://latex.artofproblemsolving.com/a/2/b/a2bce96b048c9b8fc94926db80aba37fd5037b4a.png)
of the real line, mark all integers that are divisible by at least one of the numbers 
. These points split 
into a number of smaller segments. Prove that the sum of the squares of the lengths of these segments is divisible by 
units horizontally (left or right); or
and 
,
to 
using at most 
moves.
,
be all positive integers smaller than 
such that 
for all 
is the largest positive integer that divides both 
.
such that:
such that:
is given, 
,
are graphs on the same set of 
connected components respectively. Prove that 
has at least 
connected components.
and a subset of the numbers written on the board and adds 
be real numbers . Prove that : There exist positive integer 
such that 
Where 
,
,
are pairwise distinct real numbers satisfying 
Prove that
Let 
Prove that
and 
be positive integers.
and 
.
.
Y by
I was wondering what I could use to practice for Mathcount Target rounds because my sprint is normally 23-25+ (Depending on the level: This is for Chapter, but some times for states) but my target is normally 8-10 (Depending on the level: This is normally for states and some time Nats) and I want that to go up to 12-14 So I was wondering what are some good resources to build that problem solving knowledge for target, and some resources that will help me learn the complex problems on there mostly for Geometry and Algebra.
This post has been edited 1 time. Last edited by sadas123, Mar 29, 2025, 8:17 PM
