Cryptographic Mathematics

homework

asked 2016-10-01 21:00:06 +0100

Anonymous

updated 2016-10-01 21:24:47 +0100

tmonteil
27423 ●31 ●204 ●517 http://wiki.sagemath.o...

Q: Programme Rowland’s formula and verify his results. Try different starting values and see what happens.

In Sage math cloud, I did this:

i =7
 n=2
    for n in [1..10]:
    i=i+gcd(n,i)
    print i

Could you help, please?

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i=7 n=2 for n in range(2,100): i=i+gcd(n,i) print i

sootalhzn ( 2016-10-01 23:04:16 +0100 )edit

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answered 2016-10-01 23:05:17 +0100

sootalhzn
11 ●3

Update:

i=7
n=2
for n in range(2,100):
    i=i+gcd(n,i)
    print i

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as i told before, the second line is useless
the Rowland sequence is not the list of i but i-iold.
you will get a lot of 1, so instead of printing them, you should only print the i-iold that are different from 1, use an if statement.
actually, your loop should go to 1000 or even 10000 (which makes sense only if you ignore the 1, or you won't see anything).

tmonteil ( 2016-10-02 00:05:06 +0100 )edit

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answered 2016-10-01 21:29:21 +0100

tmonteil
27423 ●31 ●204 ●517 http://wiki.sagemath.o...

updated 2016-10-01 21:45:32 +0100

Here are some hints:

please re-read Rowland's formula, the interesting sequence is not $a(n)$ but the first difference $a(n)-a(n-1)$,
If you want to see some primes appearing (not only 1's), you should look for more than only the first 10 values,
the line n=2 is useless since it is erased by the next loop, if you want to start at n=2 your loop should look like : for n in range(2,100):,
what is inside your loop should be indented
to verify the formula, you should make a test that discards the 1's appearing, and that check and prints the other if they are prime (and raise/print an error message if not).

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could you please post the code of Sage?

sootalhzn ( 2016-10-01 21:36:54 +0100 )edit

Your code is a good start, so you should get a correct code from my remarks (i updated it to be more precise). Please do not hesitate to provide some new attempts and ask for comments.

tmonteil ( 2016-10-01 21:42:44 +0100 )edit

i=7 n=2 for n in range(2,100): i=i+gcd(n,i) print i

sootalhzn ( 2016-10-01 23:02:34 +0100 )edit

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