Just a quick pat on my own shoulder…
The divisors of 12 are: 1,2,3,4,6 and 12.
The largest divisor of 12 that does not exceed the square root of 12 is 3.
We shall call the largest divisor of an integer n that does not exceed the square root of n the pseudo square root (PSR) of n.
It can be seen that PSR(3102)=47.
Let p be the product of the primes below 190.
Find PSR(p) mod 1016.
I had something much more modest in mind, such as “all primes below 100”, since the way I figured it out this was to be solved treating it as a variation of the knapsack problem and then using dynamic programming on it. An approach that will see you die of old age if you try it for the proposed value…
But I then had the pleasure of witnessing how xan, hk and daniel.is.fischer started coming up with alternative, much more sophisticated and elegant methods, that pushed the question all the way up to were it is now. It is both a humbling and edifying experience to see these people at work, so if you have an idea for a problem, do propose it to them.
I won’t go into any more details as to how to solve this particular problem: the right place to ask questions is here.