Which is the exact answer? ] a=: 5^100x 7888609052210118054117285652827862296732064351090230047702789306640625 ] b=: x: 5^100 7888609052210119712064517283480620240950194258216478103781304990433280
0. The last digit of 5^n for n>0 has to be 5. 10|a,b 5 0 1. The last 2 digits of 5x^n for n>1 have to be 25. 100 | a,b 25 80 2. The only prime that divides 5^n is 5. Try the first few primes. p: I. 0=(p: i.25)|a 5 p: I. 0=(p: i.25)|b 2 5 11 3. The only prime factor of 5^n is 5. ~. q: a 5 ~. q: b 2 5 11 1373 66923 509287 4. 5^n is */n$5x (use exact arithmetic). a = */100$5x 1 b = */100$5x 0 Not all of these generalizes to x^y . e.g. for #3, (q: x^y) -: /: y#q:x . (q: 24^132x) -: /:~ 132#q: 24 1 ----- Original Message ----- From: Roger Hui <[EMAIL PROTECTED]> Date: Friday, September 26, 2008 14:30 Subject: Re: [Jprogramming] Difference between 5^100x and x: 5^100 To: Programming forum <[email protected]> > The last digit of 5^n for n>0 has to be 5. > > 1 = 5^0 > 5 = 5^1 > > If 5^k is ...5, that is (10*m)+5, then > 5^k+1 > 5*5^k > 5*(10*m)+5 > (10*5*m)+25 > (10*2+5*m)+5 > > Similar proof for the last 2 digits of 5^n for n>1. > > > > ----- Original Message ----- > From: Ian Gorse <[EMAIL PROTECTED]> > Date: Friday, September 26, 2008 14:14 > Subject: Re: [Jprogramming] Difference between 5^100x and x: 5^100 > To: Programming forum <[email protected]> > > > > > > > As a check, you know that the last digit of 5^n for n>0 has > > > to be 5, so the x:5^100 result can not be the exact result. > > > (The last 2 digits of 5^n for n>1 have to be 25, etc.) > > > > > > > > Thanks for the reply Roger, but I have a very simple question > > regarding the quoted statement. > > > > Why? > > > > Please feel free to reply a link or search term if its out of > > scope of > > this conversation. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
