I got something interesting on this Problem.Generating X values it shows ϕ(N) for N.But i can't evaluate why this picture follows phi function.Can anyone explain me theory behind it? How co-primes are related with skipping X on this problem?
I got something interesting on this Problem.Generating X values it shows ϕ(N) for N.But i can't evaluate why this picture follows phi function.Can anyone explain me theory behind it? How co-primes are related with skipping X on this problem?
№ | Пользователь | Рейтинг |
---|---|---|
1 | tourist | 3690 |
2 | jiangly | 3647 |
3 | Benq | 3581 |
4 | orzdevinwang | 3570 |
5 | Geothermal | 3569 |
5 | cnnfls_csy | 3569 |
7 | Radewoosh | 3509 |
8 | ecnerwala | 3486 |
9 | jqdai0815 | 3474 |
10 | gyh20 | 3447 |
Страны | Города | Организации | Всё → |
№ | Пользователь | Вклад |
---|---|---|
1 | maomao90 | 174 |
2 | awoo | 164 |
3 | adamant | 163 |
4 | TheScrasse | 159 |
5 | nor | 157 |
6 | maroonrk | 155 |
7 | -is-this-fft- | 152 |
8 | Petr | 146 |
8 | orz | 146 |
10 | pajenegod | 145 |
Название |
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You number the mirrors with the point of the lazer as 0, next mirror as 1 and so on. Now if you fire the lazer at mirror numbered x it passes through the mirrors x, 2x mod(n), .., nx mod(n) which are all multiples of x taken modulo n. Now let g = gcd(x, n) if g > 1 the light comes back to the source mirror after hitting n / g mirrors (as x * (n / g) mod(n) = n * (x / g) mod(n) = 0). So they are not correct choice and the avaliable mirrors left are those for which gcd(x, n) = 1. Suppose we fired at one of those mirrors and the light comes back to source mirror at kth hit, so we have k * x mod(n) = 0 as (x, n) = 1 inverse of x modulo n exist, multiplying by its inverse we get k = 0 mod(n) which means k = n.
So all those mirrors for which we have gcd(x, n) = 1 are the right choices.
"light comes back to the source mirror after hitting n / g mirrors" ....thanks a lot.