mazes of numbers

Number Theory Level pending

There is a number $N$ .

When $N$ is divided by 7 the remainder is 1.

It can be shown as mod operator.

$\begin{aligned} N &\mod 7 = 1 \\ N &\mod 9 = 2 \\ N &\mod 11= 3 \\ \end{aligned}$

What is $N$ ?

1 solution

Sunil Pradhan
Mar 23, 2014

No. = 7a + 1 = 9b + 2 = 11c + 3

7a + 1 = 9b + 2 then 9b = 7a – 1 similarly 11c + 3 = 9b + 2 then 9b = 11c + 1

11c + 1 = 7a – 1 then 11c = 7a – 2 take values of a = 1, 2, ... by trial and error when a = 49

c = (49 × 7 – 2)/11 = 31

so number is either 49 × 7 + 1 = 31 × 11 + 3 = 344