Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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
7 years ago
Ans:
Hello Student,
Please find answer to your question below

Let the remainder to be ‘R’
We have
\frac{2^{301}}{5}
\frac{2.2^{300}}{5}
\frac{2.(2^{3})^{100}}{5}
\frac{2.(8)^{100}}{5}
\frac{2.(10-2)^{100}}{5}
\frac{2.(5k-2)}{5}
2k-\frac{4}{5}
2k-1+1-\frac{4}{5}
(2k-1)+\frac{1}{5}
So remainder is 1.

dheeraj
40 Points
7 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)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free