ចំនួនអូតូម៉ហ្វីស

ក្នុងគណិតវិទ្យា ចំនួនអូតូម៉ហ្វីស(Automorphic number) គឺជាចំនួនដែលខ្ទង់ចុងក្រោយនៃការេរបស់វាដូចនឹងខ្ទង់ចុងក្រោយនៃលេខដើម ។ ឧទាហរណ៍ 5² = 25, 76² = 5776 និង 890625² = 793212890625 ។

ចំនួនអូតូម៉ហ្វីសផ្តើមដោយលេខ ១​ ​, ៥ , ៦ , ២៥ , ​៧៦ , ៣៧៦​ , ៦២៥ , ៩៣៧៦.... ។​

អោយ ចំនួនអូតូម៉ហ្វីស${\displaystyle n>1\,}$ ដែលមាន ${\displaystyle k\,}$ខ្ទង់ ចំនួនអូតូម៉ហ្វីស ${\displaystyle n'\,}$ដែលមាន2kខ្ទង់អាចត្រូវគេសំដែងដោយរូបមន្ត ${\displaystyle n'=3\cdot n^{2}-2\cdot n^{3}{\bmod {10^{2k}}}}$ ។

យ៉ាងហោចណាស់ មានចំនួនចំនួនអូតូម៉ហ្វីសដែលមាន${\displaystyle k\,}$ខ្ទង់ មួយបញ្ចប់ដោយ ៥ និងមួយផ្សេងទៀតបញ្ចប់ដោយ ៦ ។ មួយក្នុងចំនោមនោះមានទំរង់ ${\displaystyle n\equiv 0{\pmod {2^{k}}},n\equiv 1{\pmod {5^{k}}}}$ ហើងផ្សេងទៀតមានទំរង់ ${\displaystyle n\equiv 1{\pmod {2^{k}}},n\equiv 0{\pmod {5^{k}}}}$ ។ ផលបូកនៃពីរចំនួននោះគឺ ${\displaystyle 10^{k}+1\,}$ ។

តារាងនៃចំនួនអូតូម៉ហ្វីស

n	n^2
5	25
25	625
625	390625
90625	8212890625
890625	793212890625
2890625	8355712890625
12890625	166168212890625
212890625	45322418212890625
8212890625	67451572418212890625
18212890625	331709384918212890625
918212890625	843114912509918212890625
9918212890625	98370946943759918212890625
59918212890625	3590192236006259918212890625
259918212890625	67557477392256259918212890625
6259918212890625	39186576032079756259918212890625
56259918212890625	3165178397321142256259918212890625
256259918212890625	65669145682477392256259918212890625
2256259918212890625	5090708818534039892256259918212890625
92256259918212890625	8511217494096854352392256259918212890625
392256259918212890625	153864973445024588727392256259918212890625
7392256259918212890625	54645452612300005057477392256259918212890625
77392256259918212890625	5989561329000849809744977392256259918212890625
977392256259918212890625	955295622596853633012869977392256259918212890625
9977392256259918212890625	99548356235275381465044119977392256259918212890625
19977392256259918212890625	399096201360473745722856619977392256259918212890625
619977392256259918212890625	384371966908872375601191606619977392256259918212890625
6619977392256259918212890625	43824100673983991394155879106619977392256259918212890625
106619977392256259918212890625	11367819579125235975036734004106619977392256259918212890625
4106619977392256259918212890625	16864327638717175315320739859004106619977392256259918212890625
9004106619977392256259918212890625	81073936023920699329853843152771109004106619977392256259918212890625

n	n^2
6	36
76	5776
376	141376
9376	87909376
109376	11963109376
7109376	50543227109376
87109376	7588043387109376
787109376	619541169787109376
1787109376	3193759921787109376
81787109376	6689131260081787109376
40081787109376	1606549657881340081787109376
740081787109376	547721051611007740081787109376
3740081787109376	13988211774267263740081787109376
43740081787109376	1913194754743017343740081787109376
743740081787109376	553149309256696143743740081787109376
7743740081787109376	59965510454276227407743740081787109376
607743740081787109376	369352453608598807478607743740081787109376
2607743740081787109376	6800327413935747244982607743740081787109376
22607743740081787109376	511110077017207231620022607743740081787109376
80022607743740081787109376	6403617750108490103144731780022607743740081787109376
380022607743740081787109376	144417182396352539175410357380022607743740081787109376
3380022607743740081787109376	11424552828858793029898066613380022607743740081787109376
893380022607743740081787109376	798127864794612716138610952755893380022607743740081787109376
5893380022607743740081787109376	34731928090872050116956482046515893380022607743740081787109376
995893380022607743740081787109376	991803624372854204655478894958610995893380022607743740081787109376