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Old 2004-10-28, 11:32   #9
Andi47
 
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Oct 2004
Austria

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Quote:
Originally Posted by Bob Silverman
Some intelligent, or with an understanding of 8th grade level first year
algebra might observe that if a is odd, then 10^(ab) + 1 is divisible by
10^b+1.

What is it that compels people to blindly throw a calculator or computer
at a problem *BEFORE* doing any thinking about the mathematics involved???
I dont't know how Heck figured out the divisor 7 (maybe it's this bit of algebra you mentioned with b=1001 which gives the factors 7, 11 and 13)

I figured out 11 and 13 *without* using a calculator by looking at heck's table in this thread and by rule that 10^a+1 is divisible by 11 if a is odd.

Edit: Just to mention it: divisibility by 10^b+1 gives us the factors
10^3+1 = 7*11*13
10^9+1 = 7*11*13*19*52579

and so on for b = 239, 4649 and 239*3, 239*9, 239*4649, 239*4649*3, 4649*3, 4649*9

Last fiddled with by Andi47 on 2004-10-28 at 11:39 Reason: Just another bit of information
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