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#1

$Old$ November 1st, 2009, 11:48 AM

harkapobi $harkapobi is offline$

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$Default$ Smallest Residue Problem

Hi, I have this question and I dont really even understand what it means.

Find the smallest number x>1 such that it's residue modulo

2, 3, ..., 10

is equal to 1.

If anyone could help me get my head around what this question is asking for I would be very grateful.

Thanks
Katy

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#2

$Old$ November 1st, 2009, 06:42 PM

proscientia $proscientia is offline$

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$x-1$ is divisible by $2,3,\ldots,10$ and so is divisible by ${\rm lcm(2,3,\ldots,10)}=2520.$ $\therefore\ x=2521.$

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#3

$Old$ November 2nd, 2009, 03:34 AM

harkapobi $harkapobi is offline$

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Ahh! Thank you so much! I feel pretty stupid now. lol!

Thanks

Katy

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modulo, number theory

« Least number which leaves remainder 1,2,3,4 when divided succesively by 2,3,5,7 | Top | quadratic residue problem »

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