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# What is the greatest common divisor of \$2^{1998}-1\$ and \$2^{1989}-1\$?

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What is the greatest common divisor of \$2^{1998}-1\$ and \$2^{1989}-1\$?

Oct 30, 2020

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2^1998 - 1 =3^4×7×19×73×223×1777×1999×3331×7993×10657×17539×23977×87211×169831×262657×304363×321679×1238761×25781083×26295457×36085879×319020217×473589937×616318177×5814899281×698962539799×88394945315123670399802368816023051352577985551521318859558081671366668655738553549482299216629884242626778585819274284770649396069272538413356538999183402392842975314442019321272923655248799544447055283673275666242215143015515127906359454369777040253652770303527806017975875843941430548586242460777933782626885472005549468971541624068258887410361988207308348370028082290984672424013550556006244827364709490313087534123815954202722034801442686738788221080662810713
(26 distinct prime factors, 1 distinct composite factor)

2^1989 - 1 =7×73×79×103×919×937×1327×2143×6553×8191×11119×47737×86113×121369×131071×336089287×7830118297×53607298019778595876555247053474864079403922162363705204422078695640500380868629537704192703155520542113914841675518199974609107396848464329208559905730743823182728273623242296268157009690893725622001271117420374733952099078653711939037909469078647660607567177584111510102602709122426446611921742774594407413191277420199550022528650921856305631871598849163633075573106102010715801748951249401392382569248897668089063149908100388249288510975204735432605449376146379767550161566501587127294339643313651565364676607398847140677869743
(17 prime factors, 1 composite factor)

GCD = 7  x  73 = 511

Oct 30, 2020