Latest Book Aptitude Question SOLUTION: 128^1000 divided by 153 ? remainder

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(#M40037449) BOOK Category question numbers Keep an EYE

128^1000 divided by 153 ? remainder

Asked In Book Deep Sohan Lakkad (10 years ago)

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Saraswathy  (10 years ago)

128^1000 mod 153
(2^7)^1000 mod 153
2^7000 mod 153
We can use Euler's theorem since 2 nd 153 are co-primes...
Euler value of 153 is E(153)= 96
So 2^E(153)=1
(2^96)^72 * 2^88 mod 153
1 * 2^88 mod 153

153 => 9 * 17 [a=9, b=17]
Rem[2^88/9] = r1
Rem[2^88/17] = r2

E(9) = 6
(2^6)^14 * 2^4 mod 9
1 * 16 mod 9
7 mod 9
r1 = 7

E(17) = 16
(2^16)^5 * 2^8 mod 17
1 * 256 mod 17
1 * 1 mod 7
r2 = 1

Remainder = ax+r1 = by+r2
Remainder = 9x+7 = 17y+1
Remainder = 52 [x=5, y=3]

Ans : 52

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saira fatma  (10 years ago)

i thinnk 50
128=2^7
128^1000=2^7000/153
153=3*51
=2^7000/3*51
=(-1)^7000/51
=1/51
=51-1=50

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