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The value of $3^{51} \text{ mod } 5$ is _____
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Since we get all the numbers which are less than 5 when we perform  --->>>  ( 3^x mod 5 )  when x is any positive integer so it satisfies the property of group which gets repeated after every multiple of 5.

so 3^51 mod 5  ==  (3^ (51 mod 5)) mod 5 ==  (3^1)mod 5 == 3 mod 5 = 2 , So 2 is correct ans , Unfortunately My anxiety eat that mod 5 from 3 mod 5 and I wrote 3 .
1 votes
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Lookout for last digit :
3^1=3
3^2 =9
3^3 =7
3^4 =1
3^5 =3

and the sequence  is : 3,9,7,1,3,9,7,1……………………………
at 3^51 it would be at 7. (you can see here for every multiple of 4 we are getting 1 as a last digit. so at 48 it would be “1” , at 49 it would be 3 , at 50 it would be 9 and at 51 it would be 7.)

xxxxxx7 mod 5 is as same as 7 mod 5 = 2.
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The remainders are taking an order when divided with 5.

Consider

(3 power 1) mod 5 =  2

(3 power 2) mod 5  = 4

(3 power 3) mod 5  = 2

 

This will continue for all other powers

Therefore for even number power answer will be 4 and for odd number power answer will be 2

Hence

(3 power 51) mod 5 = 2

Answer:

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