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Euler






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Challenge again...
posted on: 6/14/2006 10:55:28 PM

I am not nearly as well versed in number theory topics as I am in others, so this may be a pretty simplistic challenge, but nevertheless here it is, and if someone does solve, please feel free to post a new challenge of your own. Here it is:

Solve for a:

4a+4=3(mod 6),

(note: the equals sign should be replaced with the congruence symbol)

Have fun!
illoyd




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Challenge again...
replied on: 6/15/2006 3:35:23 AM

You put it back in its literal form:
4a+4= (n*6+3)/6 where n= 0,1,2,3 etc.

solving a = (n*2-7)/8
Euler




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Challenge again...
replied on: 6/15/2006 9:34:58 AM

Sorry, but you'll have to try again!
The Riemann Hypothesis




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Challenge again...
replied on: 6/17/2006 7:36:26 AM

4a+4 = 3 + n*6

4a = 6n - 1

a = (6n - 1)/4

??

Euler




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Challenge again...
replied on: 6/17/2006 10:33:29 PM

I would say that those question marks at the end of your post are close enough, since there is, in fact, no solution. Here is another, and this one does have a solution-

Given a and b are different integers, p and q are different primes, aq(mod p)=1, and bp(mod q)=1, then prove:

a/p + b/q > 1

Enjoy!!
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