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cosmo5

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15
Easy way to see that $(x^2 + 5x + 4)(x^2 + 5x + 6) - 48 = (x^2 + 5x + 12)(x^2 + 5x - 2)$?
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11
Where did I go wrong in applying the factor theorem?
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11
(AIME 1994) $ \lfloor \log_2 1 \rfloor + \lfloor \log_2 2 \rfloor + \ldots + \lfloor \log_2 n \rfloor = 1994 $
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11
Partition the remaining rectangle into equal parts.
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10
Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.
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9
Can $S_n=a_1a_2+a_2a_3+\cdots+a_na_1=0$ if $a_i=±1$ for $n=28$ and $n=30$?
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8
SMO problem: Sequence and series.
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7
Integral of fraction with exponentials
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7
A problem related to $\int_{0}^{1} f(x)(x-f(x))dx=1/12$
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7
Finding angle in a triangle with one median and an isosceles triangle in it
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6
summing this binomial series
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6
Suppose $x$ and $y$ are unequal real numbers
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6
Visual proof for $[\triangle ABC] = rs$?
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6
Solve integral $\int\frac{1}{(x^2-1)\sqrt{x^2+1}}dx$
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6
Probability of lines in a pentagon intersecting internally or at vertices.
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6
Exponent equation with common power
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6
Prove that the lines parallel to the angle bisectors through the midpoints of sides of a triangle are concurrent at the Spieker center
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5
Solve the inequality $x^4-3x^2+5\ge0$
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5
Number of Dispersion Lines in A Square Dot Matrix
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5
find $\lim_{n \to +\infty} \frac{-b+\sqrt{b^2 - \frac{4c}{n}}}{\frac{2}{n}}$ or prove that limit doesn't exist.
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5
Four-letter words from the word MEDITERRANEAN such that the first letter is R and the fourth letter is E
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5
Simple proof of "maximum number of right angles in a convex $n$-gon is 3 for $n\geq 5$" for a 8th grade student?
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5
Let $P$ be a $30$-sided polygon inscribed in a circle. Find the value of $\frac{N}{100}$.
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5
How many rectangles can be found in this shape?
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5
For which $n$, $n=x+y+xy$ has no solution in natural numbers?
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5
Finding solutions to $[x]^2 + 2[x]-3x=0$
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5
High school MCQ (geometry) about maximum of sine of an angle
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