Question

find the remainder when 71^175 is divided by 17​

Answer 1

Answer:

I don't know the answer just wait

Answer 2

Given:

       $71^{175} / 17$

To find :

      Remainder when dividing happen = ?

Solution:

     Remainder $[71^{175}/17]$

               ⇒  Remainder $[(85-14)^{175}/17]$  

                    (Hint : (Whole Number divisible by 17) - Remainder)

               ⇒  Remainder  $[-14^{175}/17]$

                    (Hint :  Remove the Whole number to get the Remainder)

               ⇒ Remainder     $[-537824^{35}/17]$

                   (Hint  :  Divide the power 175 by 5 and 5th  power up the -14)

               ⇒ Remainder  $[(- 537829+5)^{35}/17]$

                   (Hint:  Again step one)

               ⇒ Remainder $[5^{35}/17]$

                   (Hint : Repeat Step two)

              ⇒ Remainder $[3125^{7}/17]$

              ⇒ Remainder $[(3128-3)^{7}/17]$

                   (Hint : Remove the whole number)

             ⇒ Remainder $[-3^{7}/17]$

             ⇒ Remainder $[2187 / 17]$

             ⇒ Remainder $[(2187+6)/17]$

                 (Hint : (Number with Remainder number to make a divisible by 17)

            ⇒  6

       

   Therefore , the Remainder of 71^175 divided by 17 is 6.