New user? Sign up

Existing user? Sign in

Prove that \(m\) is an integer bigger than 11 then there always exist 2 different composite integers \(x\) and \(y\) such that \(m=x+y\).

Note by S M 1 year, 5 months ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

Sort by:

If we take \(m \equiv 0 \pmod4\), we can take \(x=8\) and y as the required multiple of 4. Note that 16 has to written as 10+6.

If we take \(m \equiv 1 \pmod4\), we can take \(x=9\) and y as the required multiple of 4.

If we take \(m \equiv 2 \pmod4\), we can take \(x=10\) and y as the required multiple of 4.

If we take \(m \equiv 3 \pmod4\), we can take \(x=15\) and y as the required multiple of 4.

Log in to reply

Great!

Depending on the intent of the question, you might be missing one small case. Note: Most people do not consider 0 a composite number.

Oh right! 15 can be written as \(6+9\).

Will you please help me out in solving a question as There is a right angle isosceles triangle ABC 90 degree angle at B and AC is hypotenuse. There are two points D, E in between AC such that AD:DE:EC=3:5:4 then prove that angle DBE=45degree

\(m>11 \\ m = 11 + a ; ~ a \in Q\\ a = \pm n, ~ n \in Q \\ m = x + y, ~x = 11, y = \pm n \)

Can you explain what you are trying to do? I have several concerns:

Ahh, is this sum that tough? I am doomed.

@S M – Nope, I am pointing out that the solution makes no sense, and does not answer the problem at all.

It's actually a pretty easy problem, just give it a try. What have you tried? Where did you get stuck?

@Calvin Lin – oh pretty sure i dont notice the condition it needs to be a composite number

@Vicky Vignesh – 13 = 9 + 4

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestIf we take \(m \equiv 0 \pmod4\), we can take \(x=8\) and y as the required multiple of 4. Note that 16 has to written as 10+6.

If we take \(m \equiv 1 \pmod4\), we can take \(x=9\) and y as the required multiple of 4.

If we take \(m \equiv 2 \pmod4\), we can take \(x=10\) and y as the required multiple of 4.

If we take \(m \equiv 3 \pmod4\), we can take \(x=15\) and y as the required multiple of 4.

Log in to reply

Great!

Depending on the intent of the question, you might be missing one small case.

Note: Most people do not consider 0 a composite number.

Log in to reply

Oh right! 15 can be written as \(6+9\).

Log in to reply

Will you please help me out in solving a question as There is a right angle isosceles triangle ABC 90 degree angle at B and AC is hypotenuse. There are two points D, E in between AC such that AD:DE:EC=3:5:4 then prove that angle DBE=45degree

Log in to reply

\(m>11 \\ m = 11 + a ; ~ a \in Q\\ a = \pm n, ~ n \in Q \\ m = x + y, ~x = 11, y = \pm n \)

Log in to reply

Can you explain what you are trying to do? I have several concerns:

Log in to reply

Ahh, is this sum that tough? I am doomed.

Log in to reply

It's actually a pretty easy problem, just give it a try. What have you tried? Where did you get stuck?

Log in to reply

Log in to reply

Log in to reply