Solution to Solve the congruence 5x≡1(mod12) Hint: 0≤x≤11 - Sikademy
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Solve the congruence 5x≡1(mod12) Hint: 0≤x≤11

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Here's the Solution to this Question

ax ≡ b(mod \space m)

Step 1

GCD of a and m

GCD of 5 & 12 

since 5 is a prime , so the GCD is 1

step 2

1/1=1

So, solutions exists

step 3

5x ≡1+12n(mod \space 12)

where n is a natural number

finding n such that (1+12n) is divided by 5

if n= 1

5x ≡1+12(mod \space 12)\\ 5x ≡13(mod \space 12)

for n=2

5x ≡1+12*2(mod \space 12)\\ 5x ≡25(mod \space 12)\\ x ≡5(mod \space 12)

So, the solution of n between 0 and 11 will be 5. In general form it will be x = 5+12m


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Question ID: mtid-5-stid-8-sqid-1301-qpid-1039