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Find Remainder when
is divided byLast edited by juantheron (2012-01-23 03:32:01)
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Answer I think is 2.
See data loop:
1 Begin 2
4
8
16
32
64
27 54
7 14
28
56
11 22
44
88
75 49 98
95 89 77 53 5 10
20
40
80
59 17 34
68
35 70
39 78
55 9 18
36
72
43 86
71 41 82
63 25 50
100
99 97 93 85 69 37 74
47 94
87 73 45 90
79 57 13 26
52
3 6
12
24
48
96
91 81 61 21 42
84
67 33 66
31 62
23 46
92
83 65 29 58
15 30
60
19 38
76
51 1 CIRCLE
igloo myrtilles fourmis
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No, I think the answer is 4.
igloo myrtilles fourmis
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The loop is 101-1 or 100 long and repeats
So 0, 100, and 200, and 2**300 is 1 for the answer.
Therefore 2**101 or 2**201 has 2 for remainder.
And 2**102 and 2**202 AND 2**302 has 4 for the remainder.
igloo myrtilles fourmis
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Woops!! I think my loop should have been 101 long not 100, so I think I should have done the power residues not on the prime # 101, but on the non-prime number of 102. This might take me longer as I don't know the proper way to do non-primes, what multiplier to use...
igloo myrtilles fourmis
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Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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I hate to be hasty, but my quick analysis of 2**y mod (3) reveals that my original answer may be correct, because it does ring around (loop around) with (3-1) or 2 numbers, so perhaps the mod(101) ring may be 100 long afterall. So I stick with my answer of 4 for the time being.
igloo myrtilles fourmis
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How did you get 2^101 mod (101) is 2, bobby?
igloo myrtilles fourmis
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Remember Fermats little theorem? It says that if you raise a number to a prime power and take the same prime modulo you get the number itself. So 2^101 mod 101 we have 101 as prime. So the answer is 2. Then you square it to get 4.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Thanks for that!!! Same answer as my power residue book too!!
igloo myrtilles fourmis
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Hi John;
Take a look at this. I know Wikipedia can be a little tough at times. It is at the top.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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I am genuinely confused that they have the coprime restriction on the second equation, making it less useful. I wonder why?
igloo myrtilles fourmis
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Hi John;
If a and p were mutiples of each other then the mods would not be one.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Yes but some non-co-primes are not multiples like 24 and 16, they share 2 thrice.
igloo myrtilles fourmis
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You are right about that. Some of them would be 0 say like 32 mod 4 = 0. We would have to guess when and when not. With the coprimes it is always true.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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I don't really complehend the whole picture of this.
What is it in summary?
igloo myrtilles fourmis
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That is a good point. We were just talking about that in another thread. We don't really need to understand mathematics to do it. My signature was written by a great mathematician. Sometimes it is like being a great carpenter. He does not know how a hammer or a chisel is made. He knows nothing about metallurgy but he does know how to use them to make beautiful things. I usually settle for that.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Nice, but that doesn't help my needy brain for greater understanding. See I tend to remember things when there is logic. Maybe I should review or do somemore examples on this modular ring power thing over the next few weeks and see if I come up with any ideas... I was planning on it anyway since I have the BASIC program to fool with.
igloo myrtilles fourmis
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Thanks to all I have also got it.
i have also use fermat Little Theorem
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I agree, I forget it all the time and have to refresh but until someone explains it to me in a way I can understand...
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Hey juantheron gets it now!!!!
igloo myrtilles fourmis
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Yeah, when it "clicks", then you remember. Something doesn't even have to be proven from ground zero, but if you can prove from some easy to remember point, then you got something.
igloo myrtilles fourmis
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I usually do not explain things unless I can put it in my own words. I hate jargon.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Hi juan;
You are welcome glad to help.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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"jargon", that reminds me it will be the year of the dragon very soon. I wonder how many days till the Chinese new year?
igloo myrtilles fourmis
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