The Mathematicat Corner Watch

Your Local Cat
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#81
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#81
(Original post by 3pointonefour)
I know which q you're talking about. How far did you get on it?
I think I did it?? N= (p_{1} ^{100} p_{2})^2
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Infinite Series
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#82
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#82
(Original post by Your Local Cat)
That was the Mathematicat Corner version 0. This is version 1.0.



yeh, although there will obviously be a little luck involved.
Is no further reading required? So would ONLY doing past papers, like what 3pointonefour mentioned, be suffice? Thanks
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#83
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#83
(Original post by Grade A)
Is no further reading required? So would ONLY doing past papers, like what 3pointonefour mentioned, be suffice? Thanks
Further reading can help, but the point of the Senior challenge is to be accessible to most people who have done gcse maths.
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3pointonefour
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#84
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#84
(Original post by Your Local Cat)
I think I did it?? N= (p_{1} ^{100} p_{2})^2
What was your method?
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Sinnoh
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#85
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#85
Why had I not followed this!?

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#86
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#86
(Original post by 3pointonefour)
What was your method?
idk how to post irl pictures so I'll show parts of the method as it takes too long to post.

(x-N)(y-N) = N^2

I think, the 2005 ordered pairs implies there are 2005 factos of N^2

2005 = 401 * 5 where gcd(401,5) = 1

Number of factors of N is (a_1 + 1)(a_2 +1)

Number of factors of N^2 is (2a_1 +1)(2a_2 +1) = 401 * 5
2 brackets since 401 and 5 are coprime.

a_1 = 200 , a_2 = 2

so N = (p_1 ^200 p_2 ^2 )

Obviously I wrote more than this.
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#87
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#87
(Original post by Sinnoh)
Why had I not followed this!?

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:askamod::ms:
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3pointonefour
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#88
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#88
(Original post by Your Local Cat)
idk how to post irl pictures so I'll show parts of the method as it takes too long to post.

(x-N)(y-N) = N^2

I think, the 2005 ordered pairs implies there are 2005 factos of N^2

2005 = 401 * 5 where gcd(401,5) = 1

Number of factors of N is (a_1 + 1)(a_2 +1)

Number of factors of N^2 is (2a_1 +1)(2a_2 +1) = 401 * 5
2 brackets since 401 and 5 are coprime.

a_1 = 200 , a_2 = 2

so N = (p_1 ^200 p_2 ^2 )

Obviously I wrote more than this.
Yeah good work that's basically it. Though I think you forgot the case where 2a_1 + 1 = 2005 (since it can just be 1 prime factor raised to the power of 2005).
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Your Local Cat
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#89
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#89
(Original post by 3pointonefour)
Yeah good work that's basically it. Though I think you forgot the case where 2a_1 + 1 = 2005 (since it can just be 1 prime factor raised to the power of 2005).
Oh yeh I considered that case but for some reason assumed that a is positive.
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Missradioactive
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#90
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#90
Gonna watch this thread 💞🤗

Your Local Cat Meow 😻
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3pointonefour
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#91
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#91
(Original post by Your Local Cat)
Oh yeh I considered that case but for some reason assumed that a is positive.
If you considered the case then I think you got the full solution. Strange how you managed this BMO2 question even though you claimed you could barely solve most Bmo1 qs lol
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#92
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#92
(Original post by 3pointonefour)
If you considered the case then I think you got the full solution. Strange how you managed this BMO2 question even though you claimed you could barely solve most Bmo1 qs lol
ooooooF
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#93
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#93
(Original post by Missradioactive)
Gonna watch this thread 💞🤗

Your Local Cat Meow 😻
k, boss
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#94
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#94
(Original post by Your Local Cat)
k, boss
:hat2: :nothing:
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#95
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#95
(Original post by Your Local Cat)
idk how to post irl pictures so I'll show parts of the method as it takes too long to post.

(x-N)(y-N) = N^2

I think, the 2005 ordered pairs implies there are 2005 factos of N^2

2005 = 401 * 5 where gcd(401,5) = 1

Number of factors of N is (a_1 + 1)(a_2 +1)

Number of factors of N^2 is (2a_1 +1)(2a_2 +1) = 401 * 5
2 brackets since 401 and 5 are coprime.

a_1 = 200 , a_2 = 2

so N = (p_1 ^200 p_2 ^2 )

Obviously I wrote more than this.
:afraid: :getmecoat:
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Notnek
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#96
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#96
(Original post by Your Local Cat)
That was the Mathematicat Corner version 0. This is version 1.0.
Seems like the new version has a few bugs. Also, I'd like to see a lot more grade growing in this thread :fuhrer:
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#97
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#97
(Original post by Notnek)
Seems like the new version has a few bugs. Also, I'd like to see a lot more grade growing in this thread :fuhrer:
I've been procrastinating the sciences :emo:
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username3989988
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#98
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#98
Your Local Cat The image didn't work, I have a page of text. :rofl:
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#99
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#99
(Original post by MaizieAmyr)
Your Local Cat The image didn't work, I have a page of text. :rofl:
feelsbad
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#100
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#100
:nyan:
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