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 ?

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## Comments

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TopNewestHow did you guys split 819529?

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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?

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If

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

301

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My ans is also $301$ vaiia

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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) .

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I think it is not correct

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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.

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$0\leq b\leq 300$ so

bhas $301$ choices. Jhon G. has already said that.Log in to reply

$a$ can be $0$, but when you type about non-negative, positive integers, one should assume that $b \gt 0$.

Granted,Log in to reply

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

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

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

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