Counter-example???I hope not!!

Is the integer n = 2 10 ( 2 11 1 ) n = 2^{10}(2^{11}-1) not \textbf{not} a perfect number??

Hint: \textbf{Hint:} 2 11 1 = 23 89 2^{11} - 1 = 23*89

No Yes insufficient information Maybe

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2 solutions

Eddie The Head
Apr 18, 2014

Solution Outline: \textbf{Solution Outline:}

Since 2 11 1 = 23 89 2^{11} - 1 = 23*89 this does not fall within the theorem proved in the last note and hence it is not a perfect number.It can also be shown manually.

I totally missed the part where you said "Is the integer 2 10 ( 2 11 1 ) 2^{10}(2^{11}-1) not a perfect number?" Argh!

Mursalin Habib - 7 years, 1 month ago

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Oh and the multiplication symbol looks more like a decimal point.

Mursalin Habib - 7 years, 1 month ago

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Exactly, it doesn't look, it is a decimal point, I requested a clarification. You should edit the problem

Beakal Tiliksew - 7 years, 1 month ago

Fixed!!

Eddie The Head - 7 years, 1 month ago

I knew the answer, but got it wrong because it wasn't clearly phrased!

Steven Perkins - 7 years, 1 month ago

The question seemed it was saying it a perfect number but I read the question and it said ^not power and so U answered no.

Mardokay Mosazghi - 7 years, 1 month ago

the correct ans should be NO.

Saurav Sharma - 7 years, 1 month ago

Come on!!! you could have phrased the problem more clearly, but I guess I am to blame for not reading the problem properly

Beakal Tiliksew - 7 years, 1 month ago

The language of the question. Arghhhh. :P

Ayush Gupta - 7 years, 1 month ago

Wonderfully phrased! :D I really love questions which are trickily phrased. And, thanks for taking my rating up to 1900 :)

Krishna Ar - 7 years, 1 month ago

The options are wrong.... I want my ratings back. @Calvin Lin and @Eddie The Head Please look into the matter...

Option (A) says, "No, they are not perfect"

Option (B) says, "Yes, they are not perfect"

Option (C) says, "Maybe they are perfect"

Thus, as you can see, there is an ambiguity in the options. Please change them and give me my ratings back...

Thanks

Satvik Golechha - 7 years, 1 month ago

I also thought that the symbol at place of multiplication is decimal point and got the question wrong! Please change it or most of others will get the question wrong and will do same mistake as others.

Kunal Joshi - 7 years, 1 month ago
Anand Raj
Apr 29, 2014

A s w a s p r o v e n b y E u c l i d , I f 2 n 1 i s P r i m e , T h e n 2 n 1 ( 2 n 1 ) i s a P e r f e c t N u m b e r As\quad was\quad proven\quad by\quad Euclid,\quad If\quad { 2 }^{ n }-1\quad is\quad Prime,\quad Then\quad { 2 }^{ n-1 }({ 2 }^{ n }-1)\quad is\quad a\quad Perfect\quad Number

Can you please elaborate it , I did'nt understood it

U Z - 6 years, 5 months ago

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