1015 has been divided by 1, 2, 3, 4 ... up to (including) 500. Find which division gave off the biggest remainder.

Question

mathmate · Answer

No takers?  :(
Are you in number theory or programming for this problem?

zyberg · Answer

Number theory.

mathmate · Answer

Try @kainui or @ganeshie88  they're not on, or @phi

mjdennis · Answer

As an engineer, I can brute-force the answer... mathematically, I haven't the first clue.

zyberg · Answer

I think that I have found a solution:

The biggest remainder would be when 1015 is divided by 508 (it would be 507, because 1015 = 507 + 508 and 1015/2=507.5), but 508 > 500.
Second biggest remainder would be 337, when divided by 339 (because 1015 = 2 * 338 + 339; 1015/3 = 338.(3) )

Ran a program to confirm this, the answer is right. After more than an hour the problem have been solved! ;)

mathmate · Answer

Yes, your answer is correct, both @mjdennis and I have checked that out
mod(1015,339)=338 is the biggest remainder for divisors up to 500.
And your reasoning sounds convincing too!   Congrats!

mathmate · Answer

*mod(1015,339)=337