Combinatorics in Number of Factor's Sum

The sum of the total number of factors of 999000999000, 816480816480 and 819529819529is n. How many ways can n be written as a+b\sqrt{a}+b where b is a non-negative integer?

Note by Mashrur Fazla
5 years, 8 months ago

No vote yet
6 votes

</code>...<code></code> ... <code>.">   Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> 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"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in </span>...<span></span> ... <span> or </span>...<span></span> ... <span> to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

How did you guys split 819529?

Brilliant Member - 5 years, 8 months ago

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?

bobby jim - 5 years, 8 months ago

Log in to reply

If b is a non-negative integer then b0 b \geq 0 and it gives the answer 301. Again,if b is a positive integer then b>0b > 0 and we can find 300 ways, Why non-negative positive ?

Sadman Sakib - 5 years, 8 months ago

Log in to reply

301

Adeeb Zaman - 5 years, 8 months ago

Log in to reply

My ans is also 301301 vaiia

Mashrur Fazla - 5 years, 8 months ago

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) .

indulal gopal - 5 years, 8 months ago

Log in to reply

I think it is not correct

Mashrur Fazla - 5 years, 8 months ago

Log in to reply

Is the answer Sum of total number of factors=300300 as b is a non-negative positive integer. so there are 301 possibilities.

John Gray - 5 years, 8 months ago

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.

indulal gopal - 5 years, 8 months ago

Log in to reply

@Indulal Gopal 0b3000\leq b\leq 300 so b has 301301 choices. Jhon G. has already said that.

Mashrur Fazla - 5 years, 8 months ago

Log in to reply

@Mashrur Fazla Granted, aa can be 00, but when you type about non-negative, positive integers, one should assume that b>0b \gt 0.

Ton de Moree - 5 years, 8 months ago

Log in to reply

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

Mashrur Fazla - 5 years, 8 months ago

Log in to reply

Also 1+(299)21+\sqrt{(-299)^2}, 2+(298)22+\sqrt{(-298)^2}, ... , 299+(1)2299+\sqrt{(-1)^2} for a total of 598598 ways :)

Ton de Moree - 5 years, 8 months ago

Log in to reply

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

Mashrur Fazla - 5 years, 8 months ago

Log in to reply

@Mashrur Fazla Ah, I see, my mistake :)

Ton de Moree - 5 years, 8 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...