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What is the remainder when 5^(301) is divided by 7?

 Nov 21, 2021
 #1
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+1

5^(301)  mod 7==5 - the remainder

 Nov 21, 2021
 #2
avatar+514 
+2

Hello Guest,

 

there is a calculator, namely: Remainder Calculator | The best Long Division Calculator (calculatored.com)

and the link https://www.calculatored.com/math/algebra/remainder-calculator.

I also got the remainder 5.

 

Hope that was helpful.^^

 

Straight

 Nov 21, 2021
 #3
avatar+115920 
+1

What is the remainder when 5^(301) is divided by 7?

 

Let's look for a pattern

 

5^1              5     mod7 = 5                5^(6n+1) = 5 mod 7

5^2              25     mod 7 = 4            5^(6n+2) = 4  mod 7

5^3            125   mod 7 = 6             5^(6n+3) = 6  mod 7

5^4            625  mod 7 = 2              5^(6n+4) = 2  mod 7

5^5            3125 mod 7 =3              5^(6n+5) = 3  mod 7

5^6           15625  mod 7 = 1           5^(6n) = 1  mod 7

 

7         78125 mod 7 = 5

8         390625 mod 7 =4

 

an so we have a pattern

 

301 = 1 mod 6  

so the remainder will be 5

 Nov 21, 2021

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