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Largest Prime Factor

P162008 3

N 3 hours ago by maromex

The largest prime factor of the sum $\sum_{k=1}^{11} k^5$ is $\lambda.$ Find the sum of the digits of $\lambda.$

3 replies

P162008

Yesterday at 12:04 AM

maromex

3 hours ago

Inequalities

sqing 27

N 4 hours ago by sqing

Let $a,b>0$ . Prove that
$\frac{a}{a^2+a +2b+1}+ \frac{b}{b^2+2a +b+1} \leq \frac{2}{5}$ $\frac{a}{a^2+2a +b+1}+ \frac{b}{b^2+a +2b+1} \leq \frac{2}{5}$

27 replies

sqing

May 13, 2025

sqing

4 hours ago

Divisors of factorials can't be always products of consecutive integers

Johann Peter Dirichlet 0

4 hours ago

Let $M$ an even number.

Show that $\frac{n!}{M^2}$ is not the product of consecutive integers for infinitely many naturals $n$ .

0 replies

Johann Peter Dirichlet

4 hours ago

0 replies

IOQM P22 2024

SomeonecoolLovesMaths 3

N Yesterday at 10:51 PM by SomeonecoolLovesMaths

In a triangle $ABC$ , $\angle BAC = 90^{\circ}$ . Let $D$ be the point on $BC$ such that $AB + BD = AC + CD$ . Suppose $BD : DC = 2:1$ . if $\frac{AC}{AB} = \frac{m + \sqrt{p}}{n}$ , Where $m,n$ are relatively prime positive integers and $p$ is a prime number, determine the value of $m+n+p$ .

3 replies

SomeonecoolLovesMaths

Sep 8, 2024

SomeonecoolLovesMaths

Yesterday at 10:51 PM

AP calc?

Thayaden 30

N Yesterday at 9:53 PM by Pengu14

How are we all feeling on AP calc guys?

30 replies

Thayaden

May 20, 2025

Pengu14

Yesterday at 9:53 PM

Calculate the radius of a circle using sidelengths.

richminer 0

Yesterday at 6:17 PM

Given triangle ABC with incircle (I), with D being the touchpoint of (I) and BC. Let M be the tangent point of the A-Mixtilinear circle (internally tangent). A' is the reflection of A through I. Calculate the radius of the circle (MDA') using the side lengths of the triangle ABC.

0 replies

richminer

Yesterday at 6:17 PM

0 replies

Number of real roots

girishpimoli 0

Yesterday at 5:35 PM

Number of real roots of

$\displaystyle 2\sin(\theta)\cos(3\theta)\sin(5\theta)=-1$

0 replies

girishpimoli

Yesterday at 5:35 PM

0 replies

Factorization Ex.28a Q30

Obvious_Wind_1690 1

N Yesterday at 4:43 PM by Lankou

Please help with factorization. Given is the question

$\begin{align*} a(a+1)x^2+(a+b)xy-b(b-1)y^2\\ \end{align*}$
And the given answer is

$\begin{align*} [(a+1)x-(b-1)y][ax+by]\\ \end{align*}$
But I am unable to reach the answer.

1 reply

Obvious_Wind_1690

Yesterday at 4:17 AM

Lankou

Yesterday at 4:43 PM

Polynomials

P162008 4

N Yesterday at 4:19 PM by HAL9000sk

If $f(x)$ is a polynomial function such that $f(x) = x\sqrt{1 + (x + 1)\sqrt{1 + (x + 2)\sqrt{1 + (x + 3)\sqrt{1 + \cdots}}}}$ then

A) Degree of $f(x)$ must be greater than $2$

B) $f(-2) = 0$

C) $\sum_{r=1}^{5} \frac{1}{f(r)} = \frac{25}{42}$

D) $\sum_{r=1}^{n} \frac{1}{f(r)} = \frac{n(3n + 5)}{4(n+1)(n+2)}$

4 replies

P162008

Monday at 11:18 PM

HAL9000sk

Yesterday at 4:19 PM

hard inequality

revol_ufiaw 10

N Yesterday at 3:43 PM by sqing

Prove that $(a-b)(b-c)(c-d)(d-a)+(a-c)^2 (b-d)^2\ge 0$ for rational $a, b, c, d$ .

10 replies

revol_ufiaw

Yesterday at 1:09 PM

sqing

Yesterday at 3:43 PM

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