Question

$\text{If}17\equiv 4\left(mod13\right)\text{then}y\equiv 22\left(mod13\right)$, find y.

• A. 18
• B. 25
• C. 35
• D. 45

Answer 1

The correct option is C 35

Given: $y\equiv 22\left(mod13\right)$

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

$(a+c)\equiv (b+c)\left(modm\right)$

Given, $17\equiv 4\left(mod13\right)$
and $y\equiv 22\left(mod13\right)$
Hence, from the above theorem, we have a = 17, b = 4 and b + c = 22
i.e., c = 22 - 4 = 18
then y = a + c = 17 + 18 = 35

By comparing the above expression with the given one, we get y = 35.