Question

Solve the Congruences
15x = 12(mod 21)
a​

Answer 1

Answer:

9x=24(mod21)⟺9x=24+21k=3+21m,k,m∈Z⟹

3x=1+7k⟹x=5(mod7)

since 3⋅5=15=1(mod7)⟺3−1=5(mod7)

Step-by-step explanation:

Answer 2

Answer:

x = 5 (mod 7)

Step-by-step explanation:

By definition of the mod we have:

A = B(mod X) ⇔ A-B  is multiple of X ⇔ $\exists \,\,\, k \in \mathbb{N}$ such that A - B = Xk.

This says that,

15x - 12 is a multiple of 21

further,

15x - 12 = 21k

⇒ 5x - 4 = 7k

⇒ 7k + 4 is multiple of the five.

Which is only true for k = 3, 8, 13, 18 ........

⇒ x = 5, 12, 19, 26, 33 ........

⇒ x = 5 (mod 7)

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