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cr001's user avatar
cr001
  • Member for 8 years, 7 months
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94 votes

Why does cancelling change this equation?

36 votes
Accepted

101102103104105106..............149150? What is the remainder when divided by 9?

20 votes

Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$

14 votes
Accepted

Find area of triangle given one angle and the lengths its altitude divides the opposite side into

12 votes
Accepted

How to prove that for $a_{n+1}=\frac{a_n}{n} + \frac{n}{a_n}$ , we have $\lfloor a_n^2 \rfloor = n$?

9 votes
Accepted

Proving the inverse of a bijection is bijective

9 votes
Accepted

Given a number, how to find the length of its binary representation?

9 votes
Accepted

Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another.

8 votes

If $\sum_n^\infty a_n$ diverges such that $a_n$ converges to 0. Prove that there exists a subsequence of $a_n$ such that $\sum_k a_{n_k}$ converges.

7 votes
Accepted

Recursive sequence with square roots

7 votes

Find an integer such that when squared, the first 4 digits are '6666'.

6 votes
Accepted

Find the highlighted angle in the regular enneagon inscribed below

6 votes
Accepted

Smallest overlapping circles containing unit circles in each section - Second arrangement

6 votes
Accepted

$\lim_{(x,y)\rightarrow(0,0)}\frac{(y^2-x)^2}{y^4+x^2}$ does not exist at $(0,0)$?

6 votes
Accepted

Find out the number of solutions to the equation- $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 25$ under certain constraints

6 votes
Accepted

Prove $n! < (n/2)^n$ by induction

5 votes

How do you solve $5\sin^2(x)+8\sin x \cos x-3=0$?

5 votes
Accepted

What is the value of $a+b$ Satisfies these two equations.

5 votes
Accepted

Is there a value of $\alpha$ such that $\cot\alpha=-2\sqrt{3}\sin\alpha?$

5 votes
Accepted

Inequality for function of $\arctan(x)$

5 votes
Accepted

Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\cdots+\frac{1}{3001}<\frac{4}{3}$

5 votes
Accepted

Prove that $a^2+b^2+c^2\geqslant\frac{1}{3}$ given that $a\gt0, b\gt0, c\gt0$ and $a+b+c=1$, using existing AM GM inequality

5 votes
Accepted

How many ways are there to add up integers to $n$ such that atleast one of them equals to 1?

5 votes
Accepted

A fair die is rolled five times.

5 votes

How many different values can you get when you insert parentheses into the expression $5-1-1-1-1-1$

5 votes
Accepted

Show that for any a ∈ ℤ, 42 | $(a^7 − a).$

5 votes
Accepted

What is the probability that $\triangle ABP$ has a greater area than each of $\triangle ACP$ and $\triangle BCP$?

5 votes
Accepted

Prove inequality by induction $ n^n >(n+1)^{n-1}$

5 votes
Accepted

Prove that $gcd(n, k) = 1$ implies $n | \binom{n}{k}$

5 votes

prime numbers and natural numbers

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