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Contests & Programs
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2012 preRMO p17, roots of equation x^3 + 3x + 5 = 0
parmenides51 11
N
Today at 3:29 PM
by Pengu14
Let
be the roots of the equation
. What is the value of the expression
?



11 replies

Interesting question from Al-Khwarezmi olympiad 2024 P3, day1
Adventure1000 3
N
Today at 2:38 PM
by sqing
Find all
such that
Proposed by Ngo Van Trang, Vietnam


3 replies
Malaysia MO IDM UiTM 2025
smartvong 1
N
Today at 2:20 PM
by jasperE3
MO IDM UiTM 2025 (Category C)
Contest Description
Preliminary Round
Section A
1. Given that
such that
. Find the value of
and
.
2. Find the value of
and
such that 
3. If the value of
is
, then find the value of
.
Section B
1. Let
be the set of integers. Determine all functions
such that for all integer
:

2. The side lengths
of a triangle
are positive integers. Let
for any positive integer
.
If
and
, determine all possible perimeters of the triangle
.
Final Round
Section A
1. Given that the equation
has two roots, where one is twice of the other, find all possible values of
.
2. Let
Find the value of 
3. Find the smallest four-digit positive integer
such that
is an integer.
Section B
1. Given that
is
in triangle
, find the ratio of the side length
to the side length
.
2. Prove that
Contest Description
Malaysian intervarsity contest
Calculators are allowed.
Time: 2 hours
Age range: 18 - 25 years old
Calculators are allowed.
Time: 2 hours
Age range: 18 - 25 years old
Preliminary Round
Section A
1. Given that




2. Find the value of



3. If the value of



Section B
1. Let




2. The side lengths




If



Final Round
Section A
1. Given that the equation


2. Let


3. Find the smallest four-digit positive integer


Section B
1. Given that





2. Prove that

1 reply
Nice problem
gasgous 2
N
Today at 1:47 PM
by vincentwant
Given that the product of three integers is
.What is the least possible positive sum of the three integers?

2 replies
Angle Formed by Points on the Sides of a Triangle
xeroxia 1
N
Today at 1:28 PM
by vanstraelen
In triangle













What is the measure of

1 reply
Is this true?
Entrepreneur 1
N
Today at 12:56 PM
by revol_ufiaw
Define the
as
Prove that
is prime for all




1 reply
Geometry
AlexCenteno2007 4
N
Today at 12:05 PM
by Raul_S_Baz
Let ABC be an acute triangle and let D, E and F be the feet of the altitudes from A, B and C respectively. The straight line EF and the circumcircle of ABC intersect at P such that F is between E and P, the straight lines BP and DF intersect at Q. Show that if ED = EP then CQ and DP are parallel.
4 replies
Concurrent in a pyramid
vanstraelen 0
Today at 7:13 AM
Given a pyramid


The intersection of the diagonals of the base is point

Point

![$[CT]$](http://latex.artofproblemsolving.com/f/3/f/f3f8e9913dc696e543e6a34d169ec3deb276c84d.png)

![$[DT]$](http://latex.artofproblemsolving.com/6/d/d/6dd49550ab42ec2f047eaf4b357ac4e7d1387b1e.png)
point

![$[AT]$](http://latex.artofproblemsolving.com/6/e/3/6e397da3c2a38b457f7b3504c5cb2a488a64f3a6.png)

![$[BT]$](http://latex.artofproblemsolving.com/6/a/4/6a4b1bcea7921e762a359321ab861b6937f04782.png)
a) Prove: the four lines are concurrent in a point

b) Calulate

0 replies
