A divisibility puzzle

Found an interesting puzzle while exploring Hari’s blog As the puzzle is very small, republishing it here. Here it goes..

Find a number x when divided by n leaves a reminder n-1,
where n ranges from 1 to 10.

I just tried to do something with the basic rules of divisibility for a few minutes before the programmer in me woke up and said “Do you really want to solve the problem? You can get the solution in no time”. Python was ready to swallow the mathematician in me

ab = range(1, 15000)
for i in range(10, 1, -1):
  ab=[x for x in ab if((x%i)==(i-1))]
print ab

Solution set: [ 2519, 5039, 7559, 10079, 12599, ... ]

The interesting fact is that the difference between any two elements in the solution set is a multiple of 2520 which is the smallest natural number divisible by all numbers from 2 to 10. Subtracting 1 from 2520 makes it indivisible by every number from 2 to 10. Wow! Having found out the solution, now I back track to solve the problem. Any mathematicians out there? Please help me solve it mathematically using the rules of divisibility

Edit: Fay has given good explanation to solve this problem. See the comments.

happy new decade

I see some excitement in me this year even though I don’t like the idea that a new year is a new beginning. After all, every new day is a new fraction of its year. The same time last year, I was just leading a less meaningful life. My return to Chennai in Jan 2009 triggered the positive change I was looking for I’m unable to believe that almost one full year has passed away after that!  With the end of the most outstanding year in my life, there goes silently, the decade that completely changed my life in a way I never imagined. Just because it was good, I cannot retain it anyway Let’s move on.. Well, forgot to wish you!  I wish you a happy new decade! Unlike the usual wishes, that doesn’t literally mean “I’m not going to bother about you in the next decade”