Question

Find the remainder when 2 power 4901 is divided by 11. Please say the answer ​

Answer 1

Given :   2 power 4901 is divided by 11    ,   2⁴⁹⁰¹   divided by 11

To find :  Remainder

Solution:

1023 /11  =  93

1023 = 1024 - 1  = 2¹⁰ - 1

=>   2¹⁰ = 1023 + 1  

2⁴⁹⁰¹   = 2⁴⁹⁰⁰ *  2   =  (2¹⁰)⁴⁹⁰ * 2

= (1023 + 1)⁴⁹⁰ * 2

(1023 + 1)⁴⁹⁰   will have all terms 1023  except  last  term 1

Hence on Dividing (1023 + 1)⁴⁹⁰ with 11  will leave remainder  as all terms with 1023 are divisible by 11

Then we have a 2 to multiply

Hence Remainder = 1 * 2 =  2

remainder =  2   when 2⁴⁹⁰¹   is Divided by 11

Learn more:

find the remainder when 2^81 is divided by 17​ - Brainly.in

https://brainly.in/question/10558440

if 3²⁰¹⁷ is divided by 10 then remainder is​ - Brainly.in

https://brainly.in/question/17611165