This repost is to give certain contributors the chance to post their complete proofs.
2007-05-31 20:07:27 · 3 answers · asked by Scythian1950 7 in Science & Mathematics ➔ Mathematics
7^10000 = (7^4 )^2500 = (24*10^2 + 1)^2500
terms + (2500)(24)(10^2) + 1 = terms + (6)(10^6) +1.
Higher order" terms" contains 10^6 so that
7^10000 = 1 mod 10^6. Done.
2007-05-31 20:55:30 · answer #1 · answered by knashha 5 · 2⤊ 0⤋
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2016-11-03 07:08:36 · answer #2 · answered by Anonymous · 0⤊ 0⤋
7^4mod10^6=2401
(7^4)^5=7^20
7^20mod10^6=
2401^5mod10^6=612001
(7^20)^5=7^100
7^100mod10^6=
612001^5mod10^6=60001
(7^100)^5=7^500
7^500mod10^6=
60001^5mod10^6=300001
(7^500)^5=7^2500
7^2500mod10^6=
300001^5mod10^6=500001
(7^25000)^4=7^10000
7^10000mod10^6=
500001^4mod10^6=000001
2007-05-31 21:09:59 · answer #3 · answered by Mamad 3 · 1⤊ 0⤋