Problem Statement Let $r$, $s$, and $t$ be the three roots of the equation $8x^3 + 1001x + 2008 = 0$. Find $(r + s)^3 + (s + t)^3 + (t + r)^3$. Problem Link Solution

Problem Statement In the diagram, two circles and a square lie between a pair of parallel lines that are a distance of 400 apart. The square has a side length of 279 and one of its sides lies alo...

Problem Statement Prove that the fraction $\frac{21n+4}{14n+3}$ is irreducible for every natural number $n$. Problem Link Solution $$n \in \mathbb{N}$$ $$\text {RTP: } gcd(21n + 4, 14n +3...

Problem Statement Find the sum of all positive integers $n$ for which $n^2-19n+99$ is a perfect square. Problem Link Solution $$\text {let } k \in \mathbb{Z} \text { such that } n^2 - 19n ...

Problem Statement Let $a_n=6^{n}+8^{n}$. Determine the remainder upon dividing $a_ {83}$ by $49$. Problem Link Solution

Problem Statement The polynomial $1-x+x^2-x^3+\cdots+x^{16}-x^{17}$ may be written in the form $a_0+a_1y+a_2y^2+\cdots +a_{16}y^{16}+a_{17}y^{17}$, where $y=x+1$ and the $a_i$’s are constants. F...

Problem Statement Let $m$ and $n$ be any two odd numbers, with $n$ less than $m$. The largest integer which divides all possible numbers of the form $m^2-n^2$ is: Problem Link Solution $$m...

Problem Statement For how many integers $k$ do the parabolas with equations $y = -\dfrac{1}{8}x^2 + 4$ and $y = x^2 - k$ intersect on or above the x-axis? Problem Link Solution $$\text{let ...

Problem Statement A circle is tangent to three sides of a rectangle having side lengths 2 and 4 as shown. A diagonal of the rectangle intersects the circle at points $A$ and $B$. The length of $A...

Problem Statement Two circles of radius 10 are tangent to each other. A tangent is drawn from the centre of one of the circles to the second circle. To the nearest integer, what is the area of th...