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20-22-1-mod-1000-

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Question Number 198418 by cortano12 last updated on 19/Oct/23
20^(22) −1 = ... (mod 1000)
2022−1=…(mod1000)
Answered by BaliramKumar last updated on 19/Oct/23
((20^(22) −1)/(1000)) = ((20(20^3 )^7 −1)/(1000)) = ((20(8000)^7 −1)/(1000)) ((20(8000)^7 )/(1000)) − (1/(1000)) = (0−1) remainder ⇒ −1+1000 = 999
2022−11000=20(203)7−11000=20(8000)7−1100020(8000)71000−11000=(0−1)remainder⇒−1+1000=999

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