User Puzzled417

31 votes

4 answers

1k views

Prove that $a^{ab}+b^{bc}+c^{cd}+d^{da} \geq \pi$

inequality

asked May 6, 2016 at 20:49

13 votes

1 answer

297 views

Solve $x^n+y^n = (x+y)^n$

calculus

asked Mar 25, 2016 at 20:03

13 votes

2 answers

2k views

Prove that $n^{n^{n^{n}}}- n^{n^{n}}$ is divisible by $1989$

number-theory

asked Dec 12, 2015 at 22:41

13 votes

5 answers

2k views

Prove the fractions aren't integers

number-theory

asked May 26, 2016 at 4:49

13 votes

1 answer

270 views

Alternating sums of numbers divisible by $7$

number-theory divisibility

asked Jun 7, 2016 at 14:10

12 votes

1 answer

485 views

Prime divisors of $5a^4-5a^2+1$

number-theory

asked Jan 9, 2017 at 22:31

10 votes

3 answers

409 views

Prove that the equation $12x^2-y^2 = 1$ has no integer solutions

number-theory

asked Aug 8, 2016 at 17:26

10 votes

2 answers

735 views

Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$

elementary-number-theory contest-math divisibility gcd-and-lcm

asked Jun 13, 2016 at 15:43

9 votes

1 answer

160 views

Prove that $\dfrac{b^{n-1}a(a+b)(a+2b)\cdots(a+(n-1)b)}{n!}$ is an integer

combinatorics number-theory elementary-number-theory

asked Jul 15, 2016 at 2:13

9 votes

4 answers

196 views

Prove that $3 \le a+b+c \le 2\sqrt{3}$ in a triangle

geometry inequality

asked Jan 21, 2016 at 14:35

8 votes

2 answers

227 views

Prove that $ \lim_{x \to \infty} f^{n}(x) = 0$

calculus limits derivatives

asked Mar 20, 2016 at 17:26

7 votes

5 answers

424 views

Is $(-2)^{\sqrt{2}}$ a real number?

number-theory elementary-number-theory complex-numbers transcendental-numbers

asked Dec 14, 2015 at 16:58

7 votes

3 answers

554 views

Prove that $0 \leq ab + ac + bc - abc \leq 2.$

inequality

asked Jan 16, 2016 at 16:05

7 votes

1 answer

317 views

Is $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}$ bounded? [duplicate]

sequences-and-series

asked Jan 17, 2016 at 15:53

7 votes

3 answers

156 views

$\frac{x^2+y^2}{x+y}$ is a divisor of $1978$

number-theory

asked Jun 29, 2016 at 3:56

7 votes

3 answers

221 views

Question on the coefficients of $(1+x+x^2+x^3+x^4)^{496}$

number-theory

asked Jul 9, 2016 at 23:42

6 votes

4 answers

279 views

Prove that $10^{340} < \frac{5^{496}}{1985}$

elementary-number-theory inequality arithmetic exponentiation number-comparison

asked Jul 10, 2016 at 17:03

6 votes

2 answers

133 views

Prove that $M = \mathbb Z^+$

number-theory elementary-number-theory

asked Jun 20, 2016 at 4:15

6 votes

3 answers

251 views

When is the fraction $\frac{n+7}{2n+7}$ the square of a rational number?

elementary-number-theory diophantine-equations

asked Jan 4, 2017 at 18:03

6 votes

4 answers

603 views

Integer solutions to nonlinear system of equations $(x+1)^2+y^2 = (x+2)^2+z^2$ and $(x+2)^2+z^2 = (x+3)^2+w^2$

number-theory systems-of-equations diophantine-equations nonlinear-system

asked Jan 5, 2017 at 20:31

6 votes

5 answers

4k views

What is an integer?

number-theory terminology

asked May 16, 2016 at 4:15

6 votes

2 answers

196 views

Prove that $\left | \frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a} \right | < \frac{1}{8}.$

geometry inequality absolute-value a.m.-g.m.-inequality buffalo-way

asked Jan 21, 2016 at 15:52

6 votes

1 answer

144 views

Prove that $\prod_{i<j} (p_i^{p_j}-p_j^{p_i})$ is divisible by $5777$

number-theory

asked Jan 19, 2017 at 0:04

6 votes

0 answers

155 views

Infinitely many rational triples $(a,b,c)$ such that $a + b + c = abc = 6$

number-theory

asked Jan 20, 2017 at 20:19

5 votes

1 answer

88 views

Prove that if $(a^2+b^2+c^2+d^2)^2 > 3(a^4+b^4+c^4+d^4)$, then, using any three of them we can construct a triangle.

geometry inequality contest-math cauchy-schwarz-inequality

asked Jan 21, 2016 at 1:28

5 votes

1 answer

1k views

Prove that $\lim_{x\to\infty}\frac{1}{x}\int_{0}^xf(t)\,dt=a$ if $f$ is continuous and $\lim_{x\to\infty}f(x)=a$

calculus real-analysis

asked May 7, 2016 at 0:30

5 votes

2 answers

102 views

For what values of $n$ does every tangent line to the graph $y=x^n$ intersect the graph exactly once?

calculus

asked Mar 26, 2016 at 0:47

5 votes

4 answers

284 views

Prove $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq \frac{a+b}{a+c}+\frac{b+c}{b+a}+\frac{c+a}{c+b}.$

inequality

asked Jan 15, 2016 at 20:17

5 votes

3 answers

164 views

Is this geometry question about a pentagon correct?

geometry

asked Dec 15, 2015 at 1:23

5 votes

3 answers

221 views

What is the least number of digits in $n$?

elementary-number-theory arithmetic

asked Dec 14, 2015 at 4:50

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301 Questions

Prove that $a^{ab}+b^{bc}+c^{cd}+d^{da} \geq \pi$

Solve $x^n+y^n = (x+y)^n$

Prove that $n^{n^{n^{n}}}- n^{n^{n}}$ is divisible by $1989$

Prove the fractions aren't integers

Alternating sums of numbers divisible by $7$

Prime divisors of $5a^4-5a^2+1$

Prove that the equation $12x^2-y^2 = 1$ has no integer solutions

Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$

Prove that $\dfrac{b^{n-1}a(a+b)(a+2b)\cdots(a+(n-1)b)}{n!}$ is an integer

Prove that $3 \le a+b+c \le 2\sqrt{3}$ in a triangle

Prove that $ \lim_{x \to \infty} f^{n}(x) = 0$

Is $(-2)^{\sqrt{2}}$ a real number?

Prove that $0 \leq ab + ac + bc - abc \leq 2.$

Is $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}$ bounded? [duplicate]

$\frac{x^2+y^2}{x+y}$ is a divisor of $1978$

Question on the coefficients of $(1+x+x^2+x^3+x^4)^{496}$

Prove that $10^{340} < \frac{5^{496}}{1985}$

Prove that $M = \mathbb Z^+$

When is the fraction $\frac{n+7}{2n+7}$ the square of a rational number?

Integer solutions to nonlinear system of equations $(x+1)^2+y^2 = (x+2)^2+z^2$ and $(x+2)^2+z^2 = (x+3)^2+w^2$

What is an integer?

Prove that $\left | \frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a} \right | < \frac{1}{8}.$

Prove that $\prod_{i<j} (p_i^{p_j}-p_j^{p_i})$ is divisible by $5777$

Infinitely many rational triples $(a,b,c)$ such that $a + b + c = abc = 6$

Prove that if $(a^2+b^2+c^2+d^2)^2 > 3(a^4+b^4+c^4+d^4)$, then, using any three of them we can construct a triangle.

Prove that $\lim_{x\to\infty}\frac{1}{x}\int_{0}^xf(t)\,dt=a$ if $f$ is continuous and $\lim_{x\to\infty}f(x)=a$

For what values of $n$ does every tangent line to the graph $y=x^n$ intersect the graph exactly once?

Prove $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq \frac{a+b}{a+c}+\frac{b+c}{b+a}+\frac{c+a}{c+b}.$

Is this geometry question about a pentagon correct?

What is the least number of digits in $n$?