turkey-yks 2011 Q12

turkey-yks · Other · lys1-math Number Theory Modular Arithmetic Computation
$$\begin{aligned} & 2 ^ { x } \equiv 1 ( \bmod 7 ) \\ & 3 ^ { y } \equiv 4 ( \bmod 7 ) \end{aligned}$$
For the smallest positive integers x and y satisfying these congruences, what is the difference $y - x$?
A) 5
B) 4
C) 3
D) 2
E) 1
$$\begin{aligned}
& 2 ^ { x } \equiv 1 ( \bmod 7 ) \\
& 3 ^ { y } \equiv 4 ( \bmod 7 )
\end{aligned}$$

For the smallest positive integers x and y satisfying these congruences, what is the difference $y - x$?\\
A) 5\\
B) 4\\
C) 3\\
D) 2\\
E) 1