Question

the linear congruence 25x congruent 12(mod 100)​

Answer 1

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Answer 2

Let us know a theorem before solving the problem:

If $\mathsf{gcd(a,m)=d}$, then the linear congruence $\mathsf{ax\equiv b(mod\:m)}$ has no solution if $\mathsf{d}$ is not a divisor of $\mathsf{b}$.

If $\mathsf{d}$ be divisor of $\mathsf{b}$, then the linear congruence $\mathsf{ax\equiv b(mod\:m)}$ has $\mathsf{d}$ incongruent solutions $\mathsf{(mod\:m)}$.

Step-by-step explanation:

The given linear congruence is

$\quad\quad \mathsf{25x\equiv 12(mod\:100)}$

Here, $\mathsf{gcd(25,100)=25}$

But $\mathsf{25}$ is not a divisor of $\mathsf{12}$.

Conclusion:

Therfore from the above theorem, we can conclude that the given congruence $\mathsf{25x\equiv 12(mod\:100)}$ has no solution.