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?

#Combinatorics #MathProblem #Math

Note by Mashrur Fazla
7 years, 8 months ago

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6 votes

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Comments

How did you guys split 819529?

A Former Brilliant Member - 7 years, 8 months ago

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 - 7 years, 8 months ago

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 - 7 years, 8 months ago

301

Adeeb Zaman - 7 years, 8 months ago

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My ans is also 301301 vaiia

Mashrur Fazla - 7 years, 8 months ago

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 - 7 years, 8 months ago

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I think it is not correct

Mashrur Fazla - 7 years, 8 months ago

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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 - 7 years, 8 months ago

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 - 7 years, 8 months ago

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

Mashrur Fazla - 7 years, 8 months ago

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@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 - 7 years, 8 months ago

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

Mashrur Fazla - 7 years, 8 months ago

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 - 7 years, 8 months ago

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

Mashrur Fazla - 7 years, 8 months ago

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

Ton de Moree - 7 years, 8 months ago
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