The sum of the total number of factors of \(999000\), \(816480\) and \(819529\)is n. How many ways can n be written as \(\sqrt{a}+b\) where b is a non-negative integer?

If b is a non-negative integer then \[ b \geq 0 \] and it gives the answer 301. Again,if b is a positive integer then \[b > 0 \] and we can find 300 ways, Why non-negative positive ?

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

bis a non-negative integer then \[ b \geq 0 \] and it gives the answer 301. Again,ifbis a positive integer then \[b > 0 \] and we can find300ways, Why non-negative positive ?Log in to reply

999000=2^3 X 3^3 X 5^3 X 37

816480=2^5 X 3^6 X 5 X 7

But how did you find out 819529=743 X 1103?

Log in to reply

How did you guys split 819529?

Log in to reply

301

Log in to reply

My ans is also \(301\) vaiia

Log in to reply

Total number of ways = 299

Solution:

999000=2^3 X 3^3 X 5^3 X 37 ; total number of factors = 128

816480= 2^5 X 3^6 X 5 X 7 ; total number of factors = 168

819529 = 743 X 1103 ; total number of factors = 4

Sum of total number of factors = n= 300 ; It can be written as 1+ sqrt(299^2),

2+sqrt(298^2),............,299+sqrt(1^2) .

Log in to reply

I think it is not correct

Log in to reply

Is the answer Sum of total number of factors=\(300\) as

bis a non-negative positive integer. so there are 301 possibilities.Log in to reply

How Mashrur you got 301? Explain. While you post a problem dont comment like " I THINK IT IS 301". Be more transparent in reply.

Log in to reply

bhas \(301\) choices. Jhon G. has already said that.Log in to reply

Log in to reply

I request you to answer Yash T. & Bobby J. questions? It is also my question.

Log in to reply

Also \(1+\sqrt{(-299)^2}\), \(2+\sqrt{(-298)^2}\), ... , \(299+\sqrt{(-1)^2}\) for a total of \(598\) ways :)

Log in to reply

In my question there is no square.there is only \(\sqrt{a}\)

Log in to reply

Log in to reply