Congruences Assignment Help

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Congruences:

Suppose m be a positive integer, then the two integer a and b called congurent modulo ml' if a -b is divisible by m i.e.  a -b = mλ 

where λ is an positive integer.

The congruent modulo m' is described on all a, b ∈ I by a ≡ b (mod m) iff a -b = λ, λ  I+

Problem: Search all congruent solutions of 8x  6 (mod 14)

 Solution:       known 8x ≡ 6 (mod 14)

                      1799_Congruences.png

                        and here greatest common divisor of 14 and 8  is 2 so, there are two needed solutions

                        for λ = 3 and λ = 7, x = 6, 13

 

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