Question

what is value of c in the following equation note c >= 0 c == -23 mod 7

Answer 1

$\textbf{Answer: }$

$\text{c=5}$

$\underline{\textbf{Skills needed: Modular arithmetic}}$

$\textbf{Step-by-step explanation below: }$

1) $\text{c is the remainder of: } -23 \div 7 \text{, but c has to be positive}$

2) $\text{We immediately know that 7 * -3 = -21, and that c can equal -2} \\ \text{but c has to be positive}$

3) $\text{Our best bet, is to add another negative 7 to 7*-3} \\ \text{This means that we are multiplying 7 by -4}$

4) $\text{7*-4 is -28, which means that c is 5 in this new case} \\ \text{Therefore, c is 5 }$

5) $\text{Hope you understand, and have a nice day!}$