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Bunuel
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If n = p^2m where p is a prime number greater than 2, how many differe 07 Dec 2020, 06:15
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D
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25% (medium)

Question Stats:

66% (01:01) correct 34% (01:06) wrong based on 196 sessions

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If n = p^2 where p is a prime number greater than 2, how many different positive odd divisors does n have, including n?

A. 0
B. 1
C. 2
D. 3
E. 4
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D
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If n = p^2m where p is a prime number greater than 2, how many differe 07 Dec 2020, 06:36
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Hi Buneul isn’t Seth wrong with this question . It’s not known whether m is prime or not , not sure if we can solve this q , pls check in case u missed smith here

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If n = p^2m where p is a prime number greater than 2, how many differe 17 Dec 2020, 22:22
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Bunuel
If n = p^2m where p is a prime number greater than 2, how many different positive odd divisors does n have, including n?

A. 0
B. 1
C. 2
D. 3
E. 4

Bunuel,

It seems there is a small typo, for the answer to be D, m should not be present.
if m is present then number of odd factors will vary depending upon the value of m.
Hope you will look into this. Thank you.
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If n = p^2m where p is a prime number greater than 2, how many differe 18 Dec 2020, 00:14
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stne
Bunuel
If n = p^2m where p is a prime number greater than 2, how many different positive odd divisors does n have, including n?

A. 0
B. 1
C. 2
D. 3
E. 4

Bunuel,

It seems there is a small typo, for the answer to be D, m should not be present.
if m is present then number of odd factors will vary depending upon the value of m.
Hope you will look into this. Thank you.
__________________
Fixed that. Thank you!
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If n = p^2m where p is a prime number greater than 2, how many differe 18 Dec 2020, 05:36
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\(n = p^2\)

For p = 3: n = 9 [odd divisors are: 1, 3, 9]

For p = 5: n = 25 [odd divisors are: 1, 5, 25]

Answer D
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If n = p^2m where p is a prime number greater than 2, how many differe 19 Dec 2020, 05:44
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Bunuel
If n = p^2 where p is a prime number greater than 2, how many different positive odd divisors does n have, including n?

A. 0
B. 1
C. 2
D. 3
E. 4

Let, \(P=3\)

\(n=3^2=9\)

The divisor of \(9 \ are: 9, 3, \ and \ 1: Total \ numbers=3\)

The answer is \(D\)

A general rule is that a Square of a prime will have exactly three divisors. So, the answer is D.
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If n = p^2m where p is a prime number greater than 2, how many differe 19 Jul 2022, 15:57
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there is a general rule that a prime number has 2 factors (3=1;3) a squared prime number has 3 factors (3^2=9=1;3;9), a cubed prime number have 4 factors (3^3=27=1;3;9;27) and so on.

If p is prime and n=(prime)^2, then it will have 3 factors.

IMO D
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If n = p^2m where p is a prime number greater than 2, how many differe 19 Jul 2022, 18:26
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Bunuel
If n = p^2 where p is a prime number greater than 2, how many different positive odd divisors does n have, including n?

A. 0
B. 1
C. 2
D. 3
E. 4

Since p is greater than 2, \(p^2\) is odd, which means every positive divisor of \(p^2\) is odd. So we simply need to determine the number of factors of \(p^2\). We can either increase the exponent of every prime in the prime decomposition of \( n = p^2\) by 1 (and obtain 2 + 1 = 3), or we can simply note that the only factors of \(p^2\) are 1, p, and \(p^2\). Using either method, we see that \(p^2\) has 3 different positive odd divisors.

Answer: D
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