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Sum of The Positive Integral Divisors
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Sum of The Positive Integral Divisors
by PokémonMaster » Tue Feb 12, 2013 7:08 pm
Okay, I know how to solve this, but does anybody know why the trick works? I am probably overlooking something simple, but an explanation would be very much appreciated. :D
UIL C 2013-14
NS: 298
Calculator: 240
Math: 282
Science: disheartening
NS: 298
Calculator: 240
Math: 282
Science: disheartening
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Re: Sum of The Positive Integral Divisors
by nsguy1350 » Tue Feb 12, 2013 7:37 pm
The shortcut is to multiply the terms [unparseable or potentially dangerous latex formula] for each term [unparseable or potentially dangerous latex formula] in the prime factorization of a number [unparseable or potentially dangerous latex formula].
Expanding this out, you get [unparseable or potentially dangerous latex formula] [unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]
This is somewhat difficult to see at first, but if you expanded this out fully, you would get the sum of all possible products of combinations of powers (likely badly worded there) that divide [unparseable or potentially dangerous latex formula], which ultimately gives you the sum of all of the positive integral divisors of [unparseable or potentially dangerous latex formula].
Expanding this out, you get [unparseable or potentially dangerous latex formula] [unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]
This is somewhat difficult to see at first, but if you expanded this out fully, you would get the sum of all possible products of combinations of powers (likely badly worded there) that divide [unparseable or potentially dangerous latex formula], which ultimately gives you the sum of all of the positive integral divisors of [unparseable or potentially dangerous latex formula].
2013 District 1/Region:
NS - 319/355
MA - 340/332
CA - 294/287
SC - 344/292
CS - 212/124 (fail)
NS - 319/355
MA - 340/332
CA - 294/287
SC - 344/292
CS - 212/124 (fail)
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Re: Sum of The Positive Integral Divisors
by PokémonMaster » Tue Feb 12, 2013 8:37 pm
Ahh, okay. I would have never thought of that. Thanks!
UIL C 2013-14
NS: 298
Calculator: 240
Math: 282
Science: disheartening
NS: 298
Calculator: 240
Math: 282
Science: disheartening
-
PokémonMaster - Incessant Spammer
- Posts: 266
- Joined: Fri Jan 27, 2012 7:20 am
- Location: Mission,Texas
Re: Sum of The Positive Integral Divisors
by 101dalmatians » Tue Feb 12, 2013 8:43 pm
I guess this signature really doesn't matter now that I know that the forum is going down soon...
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101dalmatians - Ubiquitous Spammer
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Re: Sum of The Positive Integral Divisors
by PolyMorph » Sat Mar 16, 2013 11:23 pm
Umm.. can you post an example
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