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recurrence-relations

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Is there any branch of Mathematics which has no applications in any other field or in real world?

Jan 26, 2013

Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer

Feb 8, 2013

Why can't you square both sides of an equation?

Nov 16, 2013

Collection of surprising identities and equations.

Sep 26, 2013

prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit

Dec 30, 2012

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367

Collection of surprising identities and equations.

Sep 26, 2013

When is $2^n \pm 1$ a perfect power

Sep 21, 2013

For polynomial $f$, does $f$(rational) = rational$^2$ always imply that $f(x) = g(x)^2$?

Jul 3, 2013

Odd perfect squares whose decimal representation consist only of 1's and o's

Jul 5, 2013

For what $n$ can we find a degree $\leq n-2$ polynomial such that $P(i) \in \{0 , 1 \}$ for $i \in [n]$, but not all identical.

Feb 22, 2023

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#89 this year

+10

Using $\tan 5\theta = \dfrac{5\tan\theta - 10\tan^3\theta + \tan^5\theta }{1 - 10\tan^2\theta + 5\tan^4\theta}$ solve $x^4 -10x^2 + 5 = 0$

+25

Let $x_0 = 3;\ x_{n+1}=3x_n\ $ if $\ \frac{x_n}{2}<1;\ x_{n+1}=\frac{x_n}{2}\ $ if $\ \frac{x_n}{2}>1.\ $ Is $\ \liminf_{n\to\infty} x_n=1?$

+10

When is $2^n \pm 1$ a perfect power

+10

When is $2^n \pm 1$ a perfect power

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