I do not know how to calculate this problem
$(53 \cdot d) \mod 3432 = 1$
Given this, what is the value of $d$?
I do not know how to calculate this problem
$(53 \cdot d) \mod 3432 = 1$
Given this, what is the value of $d$?
What you are trying to find is called 'the multiplicative inverse' of $53$ modulo $3432$.
Using euclidean algorithm: $\begin{align*} 3432 &= 64\cdot53 + 40\\ 53&=1\cdot40+13\\ 40&=3\cdot13+1 \end{align*}$
Now, reverse:
$\begin{align*} 1&=40-3\cdot13\\ 1&=40-3\cdot(53-1\cdot40)\\ 1&=4\cdot40-3\cdot53\\ 1&=4\cdot(3432-64\cdot53)-3\cdot53\\ 1&=4\cdot3432 - 259\cdot53 \end{align*}$
Hence $d=-259$
If you need $d>0$ use $d=3432-259=3173$
I forgot to mention: $\forall k \in \mathbb{Z},d=-259+k\cdot3432$ is a solution.