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Hi /sci/,
I buy a math book with exercices for fun, and I need to find the bigest n in N*
For (n+10) | (n^(3)+100)
I have the correction of that but I do not understand how the author came to the conclusion that n+1=900
With this factorisation:
n^(3)+100 = (n+10)(n^(2)-10n+100)-900
I thank you for your time /sci/
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if n+10 divides n^3+100
then n^3+100=k(n+10) for some integer k
so using that and the factorisation you have
n^3+100=k(n+10)=(n+10)(n^(2)-10n+100)-900
rearranging gives
-900
=k(n+10)-(n+10)(n^(2)-10n+100)
=(n+10)[k-(n^(2)-10n+100)]
and so n+10 divides -900 (equivalently n+10 divides 900)
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>>8731424
>thank you for your time
oh sweet summerchild
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>>8731424
Ah la baguette, qu'elle est belle!
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>>8731462
its a typo, it should be n+10=900
especially since (890^3+100)/(890+10)=783299 while (899^3+100)/(899+10)=80730311/101
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>>8731468
Si therefore as 900 is the bigest | to itself n+10=900
CQFD
Thank you for your help!
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>>8731459
Since there are no ugly letters, I assume OP is swiss, not french.
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>>8731479
Nope I'm French
What are our ugly letters?
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>>8731480
The c with a hook for example.
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