User S.C.B.

44 votes

Multiple-choice: sum of primes below $1000$

answered Jan 30, 2017 at 1:48

35 votes

Prove that 10101...10101 is NOT a prime.

answered Feb 11, 2016 at 0:09

32 votes

Accepted

What is a square root?

answered Mar 7, 2016 at 13:37

25 votes

How to prove that $\frac{1000!}{(500!)^2}$ is not divisible by 7?

answered Jan 24, 2017 at 15:30

20 votes

Accepted

Prove $\frac{a^3+b^3+c^3}{3}\frac{a^7+b^7+c^7}{7} = \left(\frac{a^5+b^5+c^5}{5}\right)^2$ if $a+b+c=0$

answered Feb 18, 2016 at 6:18

18 votes

Sum of all Fibonacci numbers $1+1+2+3+5+8+\cdots = -1$?

answered Jan 4, 2018 at 8:28

17 votes

Finding how many 8-bit bytes contain an even number of zeros . . .

answered Mar 6, 2016 at 17:10

15 votes

Accepted

Evaluate the limit at infinity

answered Feb 17, 2017 at 15:48

13 votes

Accepted

Simple method to solve a geometry question for junior high school student

answered Mar 13, 2016 at 3:29

12 votes

Accepted

Handshakes in a party

answered Feb 21, 2016 at 7:13

11 votes

$P(x)=\frac{x}{x+1}$ for $x=1,2,...,n$, find the value of $P(n+1)$.

answered Sep 3, 2016 at 14:32

11 votes

Accepted

Number of ways of visiting N places

answered Apr 29, 2016 at 6:52

11 votes

Why does "$x^2 - 5x + 6 = 0$", which is the same as "$(x-3)(x-2) = 0$", represent a parabola?

answered Feb 17, 2017 at 7:13

11 votes

Accepted

Show that $45<x_{1000}<45.1$

answered Jan 28, 2017 at 13:45

10 votes

Accepted

Find $x$ positive integer such that $x^4+x^3+x^2+x+1$ is a perfect square

answered Jan 28, 2017 at 13:49

10 votes

Accepted

Composition of Piecewise Function Limit

answered Feb 19, 2017 at 14:34

10 votes

Accepted

Prove that $a<b+\epsilon$ for all $\epsilon>0$ implies $a\le b$

answered Feb 22, 2017 at 11:08

10 votes

Accepted

Prove the inequality $\frac{a+c}{a+b}+\frac{b+d}{b+c}+\frac{c+a}{c+d}+\frac{d+b}{d+a}\geq 4$

answered May 1, 2016 at 7:00

10 votes

Proof of an inequality using Cauchy's inequality: $\sum_{k=1}^n \left(p_k+\frac{1}{p_k}\right)^2\geq n^3+2n+\frac{1}{n}$

answered Jan 17, 2017 at 5:44

10 votes

Accepted

Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$

answered Mar 27, 2016 at 1:11

9 votes

What is $\gcd(n-1,n+10)$, for $n$ a natural number?

answered Mar 21, 2016 at 14:37

9 votes

Accepted

Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$

answered Apr 28, 2016 at 3:47

9 votes

Prove that it is impossible to have integers $b=5a$ under a digit re-ordering

answered Feb 21, 2017 at 1:07

9 votes

Accepted

How to solve this limit without L'Hospital?

answered Feb 17, 2017 at 15:43

9 votes

Accepted

Could be this : $7131372917538397234773191167617941438959$ written as $x^{2}+y^{2}$ with $x, y$ integers?

answered Feb 8, 2017 at 15:41

9 votes

Accepted

Can both $n+3\; \text{and}\; n^2+3$ both be cubic numbers at same time?

answered Jan 31, 2017 at 6:36

8 votes

Accepted

Prove that $\sum\limits_{cyc} a^7 \geq \sum\limits_{cyc}a^4b^3$

answered Jan 29, 2017 at 14:56

8 votes

How come e becomes ln()

answered Feb 4, 2017 at 16:20

8 votes

Accepted

What does [x] mean, in this context?

answered Feb 5, 2017 at 11:52

8 votes

Accepted

If $f(x)=x+ \int_{0}^{1} t(x+t)f(t)dt$, find $\int_{0}^{1} f(x).dx$

answered Feb 5, 2017 at 16:05

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494 Answers

Multiple-choice: sum of primes below $1000$

Prove that 10101...10101 is NOT a prime.

What is a square root?

How to prove that $\frac{1000!}{(500!)^2}$ is not divisible by 7?

Prove $\frac{a^3+b^3+c^3}{3}\frac{a^7+b^7+c^7}{7} = \left(\frac{a^5+b^5+c^5}{5}\right)^2$ if $a+b+c=0$

Sum of all Fibonacci numbers $1+1+2+3+5+8+\cdots = -1$?

Finding how many 8-bit bytes contain an even number of zeros . . .

Evaluate the limit at infinity

Simple method to solve a geometry question for junior high school student

Handshakes in a party

$P(x)=\frac{x}{x+1}$ for $x=1,2,...,n$, find the value of $P(n+1)$.

Number of ways of visiting N places

Why does "$x^2 - 5x + 6 = 0$", which is the same as "$(x-3)(x-2) = 0$", represent a parabola?

Show that $45<x_{1000}<45.1$

Find $x$ positive integer such that $x^4+x^3+x^2+x+1$ is a perfect square

Composition of Piecewise Function Limit

Prove that $a<b+\epsilon$ for all $\epsilon>0$ implies $a\le b$

Prove the inequality $\frac{a+c}{a+b}+\frac{b+d}{b+c}+\frac{c+a}{c+d}+\frac{d+b}{d+a}\geq 4$

Proof of an inequality using Cauchy's inequality: $\sum_{k=1}^n \left(p_k+\frac{1}{p_k}\right)^2\geq n^3+2n+\frac{1}{n}$

Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$

What is $\gcd(n-1,n+10)$, for $n$ a natural number?

Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$

Prove that it is impossible to have integers $b=5a$ under a digit re-ordering

How to solve this limit without L'Hospital?

Could be this : $7131372917538397234773191167617941438959$ written as $x^{2}+y^{2}$ with $x, y$ integers?

Can both $n+3\; \text{and}\; n^2+3$ both be cubic numbers at same time?

Prove that $\sum\limits_{cyc} a^7 \geq \sum\limits_{cyc}a^4b^3$

How come e becomes ln()

What does [x] mean, in this context?

If $f(x)=x+ \int_{0}^{1} t(x+t)f(t)dt$, find $\int_{0}^{1} f(x).dx$