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Puzzled417
  • Member for 6 years, 5 months
  • Last seen more than 5 years ago
31 votes
4 answers
1k views

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

13 votes
1 answer
297 views

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

13 votes
2 answers
2k views

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

13 votes
5 answers
2k views

Prove the fractions aren't integers

13 votes
1 answer
270 views

Alternating sums of numbers divisible by $7$

12 votes
1 answer
485 views

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

10 votes
3 answers
409 views

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

10 votes
2 answers
735 views

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

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

9 votes
4 answers
196 views

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

8 votes
2 answers
227 views

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

7 votes
5 answers
424 views

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

7 votes
3 answers
554 views

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

7 votes
1 answer
317 views

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

7 votes
3 answers
156 views

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

7 votes
3 answers
221 views

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

6 votes
4 answers
279 views

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

6 votes
2 answers
133 views

Prove that $M = \mathbb Z^+$

6 votes
3 answers
251 views

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

6 votes
4 answers
603 views

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

6 votes
5 answers
4k views

What is an integer?

6 votes
2 answers
196 views

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

6 votes
1 answer
144 views

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

6 votes
0 answers
155 views

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

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.

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 $\lim_{x\to\infty}f(x)=a$

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?

5 votes
4 answers
284 views

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

5 votes
3 answers
164 views

Is this geometry question about a pentagon correct?

5 votes
3 answers
221 views

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

1
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11