Another remainder problem

Number Theory Level pending

Find the sum of all four-digit numbers that give a remainder of 47 when divided by 197, and a remainder of 37 when divided by 198.

1 solution

Kushal Bose
Feb 24, 2017

Assume that the four-digit number is $N$

According to the question $197m+47=198l+37=N\\ =>197m+10=198l \\ =>197(m-l)=l-10$

As $197$ is a prime number so $197 | l-10$

So, $l=10,207,404,.......$

The four digit number will be for $l=10$ and the number is $N=2017$

Great solution!

Djordje Veljkovic - 4 years, 3 months ago