Latest self Aptitude Question SOLUTION: 32^32^32 if divided by 7.what will be the remainder?

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32^32^32 if divided by 7.what will be the remainder?

Abhijit (11 years ago)

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SDeep Bhattacharya  (11 years ago)

At first,one point should be cleared that 32^32^32 and (32^32)^32 carry different meanings from each other.And according to the prob. we have to work with 32^32^32.
Now,32 =(7*4)+4
So,{(7*4)+4}^32^32 = (4^32^32)mod7.
Now, observe that 32^32 =(33-1)^32 which is definitely of the form (3A+1),where A is a +ve integer,but A's value isn't important to know here.
SO,
(4^32^32)mod7 = (4^{3A+1})mod7 ={[4^(3A)]*4}mod7 ={[64^A]*4}mod7 =
{[(7*9 +1)^A]*4}mod7 = [(1^A)*4]mod7 = 4mod7 .

So,the remainder will be 4 .

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PARAG KAMRA  (11 years ago)

32^32^32 if divided by 7
first take 32^32 means 32 is a number having power 32
32^32 mod 7=(7*4+4)^32=(7*4)^32 will give remainder 0,so take only (4)^32
((4)^2)^16 mod 7=(16)^16=(7*2+2)^16 mod 7=(2)^16 mod 7=((2)^4)^4 mod 7=(7*2+2)^4 mod 7=(2)^4 mod 7=8 mod 7=1
now next
(1)^32=1 will be remainder(ans)

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