Question

3y mod 20= 1 ,find y?
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Answer 1

Given :   3y mod 20= 1

To Find :  y

Solution:

3y mod 20= 1

=> (( 3 mod 20) (y mod 20)) mod 20  = 1

=>  ( 3 (y mod 20) ) mod 20 = 1

=>  3(y mod 20)  = 20k  + 1  

=>   y mod 20  = (20k  + 1  )/3

=>   y mod 20  =  6k +  (2k+ 1  )/3

(2k+ 1  )/3 = n

=> 2k = 3n - 1

=>   y mod 20  =  3(3n - 1)  +  n

=>  y mod 20  =  10n  - 3

=>  y mod 20  =  7  

=>   y =  20p + 7    

y = 7 , 27  , 47 , .

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Answer 2

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3y mod 20 = 1

3 mid 20 * y mod 20 = 1

3 * y mod 20 * mod 20 = 1

3 * ymod 20 = 20k + 1

y mod 20 = 20 k + 1 / 3

y mod 20 = 6k + (2k+1)/3

(2k+1)/3=n

2k = 3n - 1

y mod 20 20 = 3(3n-1)+n

y mod 20 = 10 n -3

y mod 20 = 7

y = 20 p + 7

y = 7,27,47,67,87......and so on.