무작위 수 n을 고른 다음 다음조건을 만족하며 1이될때까지 할때 모든수가 1이(안)된다를 증명하라
when n is odd n+1, when n is even n/2
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반증 자체는 간단합니다. 어떤 n에 관해 콜라츠 추측을 유한 번 반복했을때 1이 되기 전에 n이 되는 자연수 n을 하나만 찾으면 됩니다.
2^n-x 꼴로 표현한 후 x를 이진법으로 나타내서 값이 어떻게 변화하는지를 관찰하면 위 문제는 해결됩니다. (귀찮으니 다른 분께 맡기죠)
Severity: Warning
Message: mkdir(): Permission denied
Filename: libraries/Common.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: mkdir
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: getLatexImg
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Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
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Function: require_once
Severity: Warning
Message: file_put_contents(/DATA/upload/polymath/latex/46bc8c6d1fafcc24f54c974918ef32d0.gif): failed to open stream: No such file or directory
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: mkdir(): Permission denied
Filename: libraries/Common.php
Line Number: 202
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_put_contents(/DATA/upload/polymath/latex/46bc8c6d1fafcc24f54c974918ef32d0.gif): failed to open stream: No such file or directory
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
대충 쓰겠습니다.
짝수는 어차피 2로 나누어지니까 홀수가 됩니다
홀수만 증명하면 되겠네요.
n은 홀수라 합시다.
n->n+1->
됩니다. 어차피 n 홀수니까 n이 보다 큽니다.
다시 말해서 규칙에 넣으면 수가 작아지게 되고 유한번 내에 2가 되어 1이 됩니다. 끝