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Linear Congruence     Search Engine Shortcut Examples:

3x = 7 mod 4
5y = 8 modulo 3
2x is congruent to 7 mod 17
    
x ≡ (mod )<--- Enter a mod b statement
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Solve 3x ≡ 7(mod 4)

Step 1: Calculate d = (3,4)
Checking our GCF Calculator, we see that (3,4) = 1

Step 2: We check to see if 1 | 7
7  =  7
  1

Based on this, there will be 1 solutions mod 4

Our Greatest Common factor sets up a Diophantine equation below
3x - 4y = 7

Running the Extended Euclidean Algorithm for 3 and 4, we get x = 1 and y = -1








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Tags:  congruence, equation, modulus


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