IIT JEE , AIEEE Forum - Mathematics , Algebra

nadeemoidu

1)
4^96 = 16 ^48 = (12 + 4) ^ 48
Expand by binomial theorem . all terms except 4^48 will be divisible by 6.

so the remainder will be same as that of 4^48 . continue this till u get a small no. ( here u 'll get 4^3 = 64 .

So the remainder will be 4.

2)
2^2006 = 4^ 1003 = 4 . 4^1002 = 4. 16^501 = 4. (17-1) ^501

Now apply binomial theorem .

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