Let $S = {1, 2, ..., n}$, where $n \ge 1$. Each of the $2^n$ subsets of $S$ is to be colored red or blue. (The subset itself is assigned a color and not its individual elements.) For any set $T \subseteq S$, we then write $f(T)$ for the number of subsets of T that are blue. Determine the number of colorings that satisfy the following condition: for any subsets $T_1$ and $T_2$ of $S$, \[f(T_1)f(T_2) = f(T_1 \cup T_2)f(T_1 \cap T_2).\]
Steve is piling $m \geq 1$ indistinguishable stones on the squares of an $n\times n$ grid. Each square can have an arbitrarily high pile of stones. After he finished piling his stones in some manner, he can then perform stone moves, defined as follows. Consider any four grid squares, which are corners of a rectangle, i.e. in positions $(i, k), (i, l), (j, k), (j, l)$ for some $1\leq i, j, k, l \leq n$, such that $i < j$ and $k < l$. A stone move consists of either removing one stone from each of $(i, k)$ and $(j, l)$ and moving them to $(i, l)$ and $(j, k)$ respectively,j or removing one stone from each of $(i, l)$ and $(j, k)$ and moving them to $(i, k)$ and $(j, l)$ respectively. Two ways of piling the stones are equivalent if they can be obtained from one another by a sequence of stone moves. How many different non-equivalent ways can Steve pile the stones on the grid?
Let $a, b, c, d, e$ be distinct positive integers such that $a^4 + b^4 = c^4 + d^4 = e^5$. Show that $ac + bd$ is a composite number.
Solve in positive integers $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{4}{5}$
Prove there exist infinite number of positive integer $a$ such that for any positive integer $n$, $n^4 + a$ is not a prime number.
Prove for any positive integer $n$, the fraction $\frac{21n+4}{14n+3}$ cannot be further simplified.
If integer d is not equal to 2,5 or 13. Prove: there must exist two different elements $a$ and $b$ in set {2, 5, 3, d} such that $ab -
Let $ABCD$ be a cyclic quadrilateral. Let $P, Q, R$ be the feet of the perpendiculars from $D$ to the lines $BC, CA$ and $AB$ respectively. Show that $PQ = QR$ iff the bisectors of $\angle ABC$ and $\angle ADC$ meet on $AC$.
Let $ABCD$ be a convex quadrilateral for which $AC = BD$. Equilateral triangles are constructed on the sides of the quadrilateral and pointing outward. Let $O_1, O_2, O_3, O_4$ be the centres of the triangles constructed on $AB, BC, CD,$ and $DA$ respectively. Prove that lines $O_1O_3$ and $O_2O_4$ are perpendicular.
Let $f(n)$ denote the sum of the digits of $n$. Find $f(f(f(4444^{4444})))$.
Prove that $\frac{5^{125}-1}{5^{25}-1}$ is composite.
Find all integers $a$, $b$, $c$ with $1 < a < b < c$ such that the number $(a-1)(b-1)(c-1)$ is a divisor of $(abc-1)$.
Prove that if positive integer $a$ and $b$ are such that $ab+1$ divides $a^2 + b^2$. then $$\frac{a^2+b^2}{ab+1}$$ is a square number.
Find the maximal value of $m^2+n^2$ if $m$ and $n$ are integers between $1$ and $1981$ satisfying $(n^2-mn-m^2)^2=1$.
Let $A$, $B$, $C$ and $D$ be four distinct points on a line, in that order. The circles with diameters $AC$ and $BD$ intersect at the points $X$ and $Y$. The line $XY$ meets $BC$ at the point $Z$. Let $P$ be a point on the line $XY$ different from $Z$. The line $CP$ intersects the circle with diameter $AC$ at the points $C$ and $M$, and the line $BP$ intersects the circle with diameter $BD$ at the points $B$ and $N$. Prove that the lines $AM$, $DN$ and $XY$ are concurrent
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)
Show that $x^n + 5x^{n-1} + 3 = 0$ cannot be factorized into two non-constant polynomials with integer coefficients.
Let sequence $\{a_n\}$ satisfy $a_0=0, a_1=1$, and $a_n = 2a_{n-1}+a_{n-2}$. Show that $2^k\mid n$ if and only if $2^k\mid a_n$.
Let $\{a_n\}$ be a sequence defined as $a_n=\lfloor{n\sqrt{2}}\rfloor$ where $\lfloor{x}\rfloor$ indicates the largest integer not exceeding $x$. Show that this sequence has infinitely many square numbers.
Let sequence $g(n)$ satisfy $g(1)=0, g(2)=1, g(n+2)=g(n+1)+g(n)+1$ where $n\ge 1$. Show that if $n$ is a prime greater than 5, then $n\mid g(n)[g(n)+1]$.
Seventeen people correspond by mail with one another - each one with all the rest. In their letters only three different topics are discussed. Each pair of correspondents deals with only one of these topics. Prove that there are at least three people who write to each other about the same topic.
Let $n$ be an integer greater than or equal to 3. Prove that there is a set of $n$ points in the plane such that the distance between any two points is irrational and each set of three points determines a non-degenerate triangle with rational area.
(Weitzenbock's Inequality) Let $a, b, c$, and $S$ be a triangle's three sides' lengths and its area, respectively. Show that $$a^2 + b^2 + c^2 \ge 4\sqrt{3}\cdot S$$
The diagonals $AC$ and $CD$ of the regular hexagon $ABCDEF$ are divided by inner points $M$ and $N$ such that $AM:AC = CN:CE=r$. Determine $r$ if $B, M,$ and $N$ are collinear.
Prove that there is one and only one triangle whose side lengths are consecutive integers, and one of whose angles is twice as large as another.
If a sequence $\{a_n\}$ satisfies $a_1=1$ and $a_{n+1}=\frac{1}{16}\big(1+4a_n+\sqrt{1+24a_n}\big)$, find the general term of $a_n$.