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#1 2012-12-28 01:07:17

pellerinb
Member
Registered: 2012-12-26
Posts: 43

GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1) i!) = 99 for N >= 10

Just curious if anyone else has observed this. I have found it true up to N = 1 million.

GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1)  i!) = 99 for N >= 10

I'm thinking it might be easy to prove this too... I'm not sure though.


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#2 2012-12-31 00:32:49

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,127
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Re: GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1) i!) = 99 for N >= 10

The question seems interesting, could you please make it clear with latex?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#3 2012-12-31 00:55:56

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1) i!) = 99 for N >= 10

I don't know how to input latex into this forum but I can tell you that if you enter 'sum_(i=1)^10 i! ; sum_(i=1)^11 i!' without quotes into the Wolfram|Alpha website or iPhone/iPad app, you will see the desired equations and their GCD.


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#4 2012-12-31 02:44:33

muxdemux
Member
Registered: 2012-12-23
Posts: 80

Re: GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1) i!) = 99 for N >= 10

Latex here:

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