I'm in 8th grade and my geometry teacher recommended that I read the art of problem solving. So I did and I have now read the chapter called "Integers". I am now doing some of the problems in the section and I came across this one which has stumped me. The question reads:
Find the smallest positive integer which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, by 8 leaves a remainder of 7, ect., down to where, when divided by 2, it leaves a remainder of 1.
I approached this problem by writing what the possible numbers could be. For when divided by 10 with a remainder of 9, I noticed that all the possible answers had to end in a 9 so I looked for numbers that ended in a 9 for the other conditions. For when it was divided by 2 with a remainder of 1 I concluded that it had to be the 5th, 10th, 15th, ect., term. and for when divided by 3 it had to be the 10th, 20th, ect., term. The problem is I have no idea on how I would find where all of these would fall on the same number? I am looking for a suggestion on how I would use the knowledge I already have to solve the problem.