data/problems/375.yml
---
:id: 375
:name: Minimum of subsequences
:url: https://projecteuler.net/problem=375
:content: "Let <var>S</var><sub><var>n</var></sub> be an integer sequence produced
with the following pseudo-random number generator:\n\n<center><table class=\"p375\">\n<tr>\n<td
style=\"text-align:right;\">\n<var>S</var><sub>0</sub>\n</td>\n <td>=<sub> </sub>\n</td>\n
\ <td>290797<sub> </sub>\n</td>\n </tr>\n<tr>\n<td>\n<var>S</var><sub><var>n</var>+1</sub>\n</td>\n
\ <td>=<sub> </sub>\n</td>\n <td>\n<var>S</var><sub><var>n</var></sub><sup>2</sup>
mod 50515093</td>\n </tr>\n</table></center>\n\nLet A(<var>i</var>, <var>j</var>)
be the minimum of the numbers <var>S</var><sub><var>i</var></sub>, <var>S</var><sub><var>i</var>+1</sub>,
... , <var>S</var><sub><var>j</var></sub> for <var>i</var> ≤ <var>j</var>. \nLet
M(<var>N</var>) = ΣA(<var>i</var>, <var>j</var>) for 1 ≤ <var>i</var> ≤ <var>j</var>
≤ <var>N</var>. \nWe can verify that M(10) = 432256955 and M(10 000) = 3264567774119.\n\nFind
M(2 000 000 000).\n\n"