Latest Wipro Aptitude Question SOLUTION: Find remainder of 128^1000 divided by 153??

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Find remainder of 128^1000 divided by 153??

Asked In Wipro MD (10 years ago)

Unsolved Read Solution (5)

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chaitanya  (10 years ago)

128^500, just try to divide 128 by 153, the remainder is 128 a very big no, u have to make this number smaller and smaller.
now think of 128^2 = 16384, which on division by 153 gives, 13 as the remainder.
so we can write
128^500 = ((128)^2)^250
= (13)^250 (remainder on division by 153)
= (169)^125
= (16)^125 (remainder on division by 153)
= ((16)^5)^3
= (52)^3 (remainder on dividing 16^5 = 65536 by 153 is 52)
= 140608
= 1 (Dividing 140608 by 153 leaves the remainder 1)

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Sayan Bhattacharya  (10 years ago)

we know if n=even, ((x^n)-(a^n)) is completely divisible by x+a; so...as n=1000...(128^1000-25^1000) is completely divisible by 153...so finally the remainder will be 25...

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Prateek Pandey  (10 years ago)

Well not as simple as it looks.
Charmichael number for 153 is 48
1000 mod 48= 40
128^40 or (-25)^40 or 625^20
13^20 mod 153
16^10 mod 153
keep solving little more and you'll get 52(ans)

Is this solution Helpfull? Yes (1) | No (5)  

Prateek Pandey  (10 years ago)

Easier alternative:
128=2^7
So 128^40=2^280
280 mod 48 =40
so equation is reduced to:
2^40 mod 153
(1024)^4 mod 153
106^4 mod 153
67^2 mod 153
=52

Is this solution Helpfull? Yes (1) | No (4)  

mohit  (7 years ago)

52 is the correct answer.

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