Hi there,
I'm working on a challenging puzzle which has me stumped. Here's the puzzle:
The following integers are consecutive **odd** powers of positive integer n, modulo a prime p.
- 90294841550344816920887395661747009736776650389614188142234605341400837126935378962489093789304037012868865437487922365342634723283696836637124520023049181869683469618895547182582440399365913174543225847872578172013129407552822938718555003731781986580089209691798780166234583492600874314576345541675093982137
- 42112740916772037375685254921538983911644443827842337394452880167068150594758982190383469218015976268028090254728528315130811516188594491321224583443439668701051438584579482605798009769238349101345491182202258282337139831875260201668992051044699720135353308959492194703707745594534013426741014891335870980880
- 87180918919574072205554476329837952799702171247429339727497586770094835390424317893348790803256513194120757507235333861390608969760508445506057205876811891955334356529195773541041204260787986038340782273645180474215454308964005172573507294260166685386641289134326371664778198645454685870091458817878746531813
- 66333292954178432288941676027475571830932728184361041976833108302152864435806237824011965396627497187209957429653087219620712885418961611550051600220673650628686383326072418081069989325327841047094971105949273922761137919336536404468380272474427193894169492676377106066924900762148034740644413480969423620637
.
(In other words, these are n^(2k+1) mod p, n^(2k+3) mod p, n^(2k+5) mod p, and n^(2k+7) mod p -- for some positive integer n, k and prime p.)
.
What are n and p?
Any help would be greatly appreciated.
I'm working on a challenging puzzle which has me stumped. Here's the puzzle:
The following integers are consecutive **odd** powers of positive integer n, modulo a prime p.
- 90294841550344816920887395661747009736776650389614188142234605341400837126935378962489093789304037012868865437487922365342634723283696836637124520023049181869683469618895547182582440399365913174543225847872578172013129407552822938718555003731781986580089209691798780166234583492600874314576345541675093982137
- 42112740916772037375685254921538983911644443827842337394452880167068150594758982190383469218015976268028090254728528315130811516188594491321224583443439668701051438584579482605798009769238349101345491182202258282337139831875260201668992051044699720135353308959492194703707745594534013426741014891335870980880
- 87180918919574072205554476329837952799702171247429339727497586770094835390424317893348790803256513194120757507235333861390608969760508445506057205876811891955334356529195773541041204260787986038340782273645180474215454308964005172573507294260166685386641289134326371664778198645454685870091458817878746531813
- 66333292954178432288941676027475571830932728184361041976833108302152864435806237824011965396627497187209957429653087219620712885418961611550051600220673650628686383326072418081069989325327841047094971105949273922761137919336536404468380272474427193894169492676377106066924900762148034740644413480969423620637
.
(In other words, these are n^(2k+1) mod p, n^(2k+3) mod p, n^(2k+5) mod p, and n^(2k+7) mod p -- for some positive integer n, k and prime p.)
.
What are n and p?
Any help would be greatly appreciated.