Hi Abhishek009,

I am slightly confused = is it not wrong to say that 27^28 = (26^28 + 1^28) ??

it's like saying 2^4 = (1^4 + 1^4) which comes out to be = 2 and not 16..

Please guide?

Would this same method of cyclical remainders be applicable?

3^1 = 3 --> 3/26 --> R3
3^2 = 9 --> 9/26 --> R9
3^3 = 27 --> 27/26 --> 1 R1 <---- Cycle stops here
3^4 = 81 --> 81 / 26 --> 3 R3

Given an exponent of 84 ---> 84 /3 = 26 <--- so 26 cycles of 3. Hence, the remainder is 1.
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For this type of questions for me the best approach is to use cycles. Even though sometimes could take you instead of 50 sec 1:50. This simply because is the only one among the 3 that you can apply in "many" others mid-high level problems, but just my tought.

3^1 when divided by has remainder equal to 26
3^2 9
3^3 1
3^4 3 probably cycle yet finished
3^5 9 I would be sufficiently sure and I wouldn't go ahead but your choice
so the pattern is 9, 1, 3
84 is divisible by 3 hence r = 3

I want to ask to the experts what is the binomial method and if it worth to study it

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