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#1
10-24-2002, 08:47 PM
 Jim Brier Senior Member Join Date: Sep 2002 Location: Las Vegas, NV Posts: 189
Simple Math Problem

If you take 513 and raise it to the 128th power, what is the one's digit? Is there a simple way of figuring it out?
#2
10-24-2002, 09:19 PM
 Guest Posts: n/a
Re: Simple Math Problem

If you only care about the one's digit, it only matters that 513 ends with a 3.

3^0 ends with 1
3^1 ends with 3
3^2 ends with 9
3^3 ends with 7

from here, it repeats: 1, 3, 9, 7. So simply take the power and divide by 4. The remainder should tell you which of these is the last digit.

For your example: 128 mod 4 is 0, therefore 513^128 ends with a 1.

Hope that helps!
#3
10-25-2002, 02:09 AM
 M.B.E. Senior Member Join Date: Sep 2002 Location: Vancouver, B.C. Posts: 1,552
Re: Simple Math Problem

"Anonymous" is correct. Notice that 3^4=81 so 3^128=81^32. Now when you take 81 to any whole power the ones digit can only be 1, since 1x1=1. The ones digit of 513^128 is the same as the ones digit of 3^128, which is 1.
#4
10-25-2002, 03:16 AM
 Jim Brier Senior Member Join Date: Sep 2002 Location: Las Vegas, NV Posts: 189
Thanks Guys! I love this forum! (n/t)

(n/t)
#5
10-25-2002, 04:53 AM
 Guest Posts: n/a
Re: Simple Math Problem

last semester i was in a number theory class at university, and i thought to myself while these very questions were being brought up in class...."who the hell would want to know that" well now i know

thanks for making my class not an entire waste
#6
10-25-2002, 08:31 AM
 irchans Senior Member Join Date: Sep 2002 Posts: 157
Re: Simple Math Problem

For many years number theory had no applications but since the advent of computers, many applications have arrived. Most of the applications are in encryption, but you occasionally run into number theory in other fields (e.g. CDMA for cell phone transmission, pseudo-random number generation).

PS:
513^128 =

78527674095678372984552781105929458007589456144486 82
65644231223842532332696067633795458244587461783802 15
02477421627930646460271928516001276777242677537671 02
04753715518451952675490654125302312881638160106707 57
06828700240755793013636138691904689489491326625021 94
48497782634590705850754151909775421521223364755619 37
93612817448994130470020200985067521

#7
10-25-2002, 06:17 PM
 mdlm Senior Member Join Date: Sep 2002 Posts: 187
What software did you use?

What software did you use to do this computation?
#8
10-27-2002, 09:05 PM
 irchans Senior Member Join Date: Sep 2002 Posts: 157
Re: What software did you use?

Mathematica

www.wolfram.com

(Student discounts are substantial).

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