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William Elliot
science forum Guru
Joined: 24 Mar 2005
Posts: 1906
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 Posted: Fri Jul 21, 2006 12:07 pm Post subject:
Mod computer problem
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What is the solution to
n mod 5 = n mod 7 ? |
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Pubkeybreaker
science forum Guru
Joined: 24 Mar 2005
Posts: 333
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| Posted: Fri Jul 21, 2006 12:22 pm Post subject:
Re: Mod computer problem
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William Elliot wrote:
| Quote: | What is the solution to
n mod 5 = n mod 7 ?
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"The" solution??? There are infinitely many.
Trivally, n= 1 is a solution. so is n = 2, so is n = 3. so is n =
4..
Now think about the Chinese Remainder Theorem....
(example: n = 74 is a solution; ask yourself what relation the number
74
has to one of the first 4 solutions that I gave) |
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Jussi Piitulainen
science forum beginner
Joined: 16 Jun 2005
Posts: 11
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| Posted: Fri Jul 21, 2006 12:53 pm Post subject:
Re: Mod computer problem
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William Elliot writes:
| Quote: | What is the solution to
n mod 5 = n mod 7 ?
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Guessing from the subject line that you want it solved
using a computer, here's a program to collect all k in a
given interval that satisfy the condition:
(define (loopy-do k n em)
(if (< k n)
(if (= (modulo k 5) (modulo k 7))
(loopy-do (+ k 1) n (cons k em))
(loopy-do (+ k 1) n em))
(reverse em)))
Running it for all k from -200, inclusive, to 200,
exclusive, we get a list of solutions:
| Quote: | (loopy-do -200 200 '())
'(-175 -174 -173 -172 -171 -140 -139 -138 -137 -136 -105 |
-104 -103 -102 -101 -70 -69 -68 -67 -66 -35 -34 -33 -32
-31 0 1 2 3 4 35 36 37 38 39 70 71 72 73 74 105 106 107
108 109 140 141 142 143 144 175 176 177 178 179)
The general solution seems to be 35k + {0,1,2,3,4} where k
is any integer. |
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William Elliot
science forum Guru
Joined: 24 Mar 2005
Posts: 1906
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| Posted: Fri Jul 21, 2006 1:15 pm Post subject:
Re: Mod computer problem
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On Fri, 21 Jul 2006, Jussi Piitulainen wrote:
| Quote: | William Elliot writes:
What is the solution to
n mod 5 = n mod 7 ?
Guessing from the subject line that you want it solved
using a computer, here's a program to collect all k in a
given interval that satisfy the condition:
No I didn't. n mod 5 is computerese but is tossed around like it is real |
math. Thus since computerese has pretense to math, the guess to make is a
computerese math solution.
| Quote: | (define (loopy-do k n em)
(if (< k n)
(if (= (modulo k 5) (modulo k 7))
(loopy-do (+ k 1) n (cons k em))
(loopy-do (+ k 1) n em))
(reverse em)))
Running it for all k from -200, inclusive, to 200,
exclusive, we get a list of solutions:
(loopy-do -200 200 '())
'(-175 -174 -173 -172 -171 -140 -139 -138 -137 -136 -105
-104 -103 -102 -101 -70 -69 -68 -67 -66 -35 -34 -33 -32
-31 0 1 2 3 4 35 36 37 38 39 70 71 72 73 74 105 106 107
108 109 140 141 142 143 144 175 176 177 178 179)
The general solution seems to be 35k + {0,1,2,3,4} where k
is any integer.
That's why it's not a computer program problem, but a computerese problem, |
depending upon what implementation of a mod n is in vogue That the
program won't ever give the solution set.
x mod -5 = x mod 7
is sheer computerese for there is no Z_-5 integers modulus -5
tho by scraping the bottom of the barrel, one could fantasy such.
The solution to the later equation is much more computer language
sensitive than the former equation. |
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Bill Dubuque
science forum Guru Wannabe
Joined: 04 May 2005
Posts: 236
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| Posted: Fri Jul 21, 2006 2:10 pm Post subject:
Re: Mod computer problem
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William Elliot <marsh@hevanet.remove.com> wrote:
| Quote: |
What is the solution to
n mod 5 = n mod 7 ?
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HINT n mod a = n mod b, 0 < a <= b
<-> n = n mod a + ab/(a,b) Z
If a or b = 0 use |Z/a| <= |Z/b| vs. 0 < a <= b
--Bill Dubuque |
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