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Counting problem
lgx57 1
N
by HAL9000sk
Calculate the number of 
that meet the following conditions:
1.
2.
appears exactly once in each octal digit of
that meet the following conditions:1.
2.
appears exactly once in each octal digit of
1 reply
Geometry
Arytva 0
Let 
be an acute triangle, and let its circumcircle be 
. On side 
, pick a point 
(distinct from 
and 
). The lines through tangent to (other than 
, if 
lies inside the angle at ) touch again at points 
and 
. Let 
meet 
at 
, and let 
meet 
at 
. Prove that the three lines 
, 
, and 
are concurrent.
be an acute triangle, and let its circumcircle be 
. On side 
, pick a point 
(distinct from 
and 
). The lines through tangent to (other than 
, if 
lies inside the angle at ) touch again at points 
and 
. Let 
meet 
at 
, and let 
meet 
at 
. Prove that the three lines 
, 
, and 
are concurrent.
0 replies
Easy Function
Darealzolt 1
N
by alexheinis
Let 
for all real numbers 
, hence find the value of 
if 
.
for all real numbers 
, hence find the value of 
if 
.
1 reply
Spot-It inspired question
alexroberts 1
N
by alexroberts
Oscar bought a set of blank playing cards. He puts stamps on each card such that
1. Each card has
different stamps each.
2. Every two cards have exactly one stamp in common.
3. Every stamp is used at least twice.
Show that the maximum number of different stamps
he can use is in the range 
1. Each card has
different stamps each.2. Every two cards have exactly one stamp in common.
3. Every stamp is used at least twice.
Show that the maximum number of different stamps
he can use is in the range 
1 reply
Floor of Cube Root
Magdalo 2
N
by RedFireTruck
Find the amount of natural numbers 
such that ![$\lfloor \sqrt[3]{n}\rfloor\mid n$](//latex.artofproblemsolving.com/5/6/2/562cedff73965e1dce784a360514b931e36158b1.png)
.
such that ![$\lfloor \sqrt[3]{n}\rfloor\mid n$](http://latex.artofproblemsolving.com/5/6/2/562cedff73965e1dce784a360514b931e36158b1.png)
.
2 replies
Find the value of m
Darealzolt 2
N
by RedFireTruck
Let 
be a positive integer, such that fulfills
![\[
\frac{1}{m^2+3m+2}+\frac{1}{m^2+5m+6}+\frac{1}{m^2+7m+12}+\dots +\frac{1}{m^2+15m+56}+\frac{1}{m^2+17m+72} = \frac{8}{33}
\]](//latex.artofproblemsolving.com/8/c/4/8c4821c428f4c98ce4e66b26168313739188cc03.png)
Hence find the value of .
be a positive integer, such that fulfills![\[
\frac{1}{m^2+3m+2}+\frac{1}{m^2+5m+6}+\frac{1}{m^2+7m+12}+\dots +\frac{1}{m^2+15m+56}+\frac{1}{m^2+17m+72} = \frac{8}{33}
\]](http://latex.artofproblemsolving.com/8/c/4/8c4821c428f4c98ce4e66b26168313739188cc03.png)
Hence find the value of .
2 replies
Polynomials
P162008 2
N
by RedFireTruck
P1. Find 
where 
is a monic polynomial of degree 
satisfying 
P2. Find
where is a polynomial of smallest degree possible satisfying 
P3. Find
and 
, if polynomial satisfies 
P4. Find where is a polynomial of smallest degree satisfying 
P5. Find
and 
if polynomial satisfies 
P6. If
is a polynomial of degree 
such that 
Evaluate 
where 
is a monic polynomial of degree 
satisfying 
P2. Find
where is a polynomial of smallest degree possible satisfying 
P3. Find
and 
, if polynomial satisfies 
P4. Find
where is a polynomial of smallest degree satisfying 
P5. Find
and 
if polynomial satisfies 
P6. If
is a polynomial of degree 
such that 
Evaluate 
2 replies
common tangents
gasgous 2
N
by gasgous
Find the equations of the common tangents to the circles:
and 
.
and 
.
2 replies
the Basics
wpdnjs 6
N
by kyEEcccccc
given that log base 3 of 2 is approximately 0.631, fin the smallest positivie integer a such that 3^a > 2^102.
somebody anyone pls help :wacko:
somebody anyone pls help :wacko:
6 replies
Find sets of positive integers (a,b) such that there exists a positive integer c
kyotaro 1
N
by alexheinis
Find sets of positive integers (a,b) such that there exists a positive integer c such that 
and 
.
and 
.
1 reply
