Question

find the remainder when 2^100 is divided by 3 ???

Answer 1

2^100 ÷3 = 4.22550229
please mark it as a brainliest friend

Answer 2

Method - 1:

We know that

= > 2 mod 3 = 2[2^1/3 = 2]

= > 4 mod 3 = 1[2^2/3 = 1]

= > 8 mod 3 = 2[2^3/3 = 2]

= > 16 mod 3 = 1[2^4/3 = 1]

= > 32 mod 3 = 2[2^5/3 = 2]

Now,

According to question.

= > 2^100/3

= > (2^4)^25/3

= > 1^25/3

= > 1.

Therefore, the remainder is 1.

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Method - 2:

Here, it should be in the form of a = b(mod n).

When a is divided by n, the remainder is b.

Now,

= > 2^2 = 1(mod 3)

= > (2^2)^5 = 1^5(mod 3)

= > (2^10) = 1(mod 3)

= > 2^10 = 1(mod 3)

= > (2^10)^2 = 1^2(mod 3)

= > 2^20 = 1(mod 3)

= > 2^20 = 1(mod 3)

= > (2^20)^5 = 1^5(mod 3)

= > 2^100 = 1(mod 3).

Therefore, the remainder is 1.

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Hope this helps!