what is the remainder when 2 to the power of 301 is divided by 5

what is the remainder when 2 to the power of 301   is divided by 5

Grade:12th Pass

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Hello Student,
Please find answer to your question below

Let the remainder to be ‘R’
We have
So remainder is 1.

40 Points
8 years ago
wkt (2,1)common factor is 1
so, we take 2^301-1congruent to 1(mod301)
=2^300 congruent to 1(mod301)            (let it be eqn 1)
wkt   2 is congruent to 1 (mod301)           (let it be eqn 2)
now multiply both the eqn’s and we get
  2^301 is congruent to 1(mod301)                                                             [note  here any integer before (mod n) is remainder of given number]
so,we get 1 as remainder of the given equation(eqn)

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