Question

$\text{If}9\equiv 3\left(mod6\right)\text{and}14\equiv 2\left(mod6\right)$, then $126\equiv z\left(mod6\right)$. Find z.

• A. z = 1
• B. z = 3
• C. z = 5
• D. z = 6

Answer 1

The correct option is D z = 6

Given:$126\equiv z\left(mod6\right)$

By the theorem on modulo operations, if a, b, c and d are integers and m is a positive integer such that if $a\equiv b\left(modm\right)$ and $c\equiv d\left(modm\right)$ , then
(i) $(a\times c)\equiv (b\times d)\left(modm\right)$

Given, $9\equiv 3\left(mod6\right)\text{and}14\equiv 2\left(mod6\right)$
Hence, from the (i) theorem,
$(9\times 14)\equiv (3\times 2)\left(mod6\right)$
$\Rightarrow$ $126\equiv 6\left(mod6\right)$
By comparing the above expression with the given one, we get z = 6.