remainder when 128 1000 is divided by 153

copy and pasted by mounicaoruganti from karthikeya evet single digit so not changed.....bappppre
9 years agoHelpfull: Yes(5) No(1)
Ans is:52
128^1000/153
(128^2)^500/153
(16384) by 153 reminder=13
(13^2)^250/153
=(169)/153 reminder=16
Now 16^250/153
(16^6)^41*(16^4)/153
=(16^6)=16777216/153 Reminder 1
=(16^4)=65536/153 Reminder 52
So 52*1=52
Ans is 52
9 years agoHelpfull: Yes(1) No(1)
128^1000/153
128 and 153 are coprime no.
153(1-1/17)(1-1/3)=96
=2^7000/153
=2^(96k+11)/153
=2^11/153
=2048/153
remainder=59
9 years agoHelpfull: Yes(0) No(1)
=2^(96k+88)/153
=2^88/153
as 2^7/153 = -25/153
2^88 = 2^(7*12 + 4)
= 2^4*25^12/153
= 2^4*13^6/153
=2^4*16^3/153
= 2^16/153 = 2^(7*2 + 2)/153 = 2^2*25^2/153 = 4*13 /153
remainder = 52
9 years agoHelpfull: Yes(0) No(0)
bhai ye 88 kha se aaya
9 years agoHelpfull: Yes(0) No(0)
128=8*16 (9-1)^1000/9 * (17-1)^1000/17 => (-1)^1000*(-1)^1000 =>1ans
153=9*17
9 years agoHelpfull: Yes(0) No(0)

remainder when 128^1000 is divided by 153?