Chinese leftovers II
Problem 552
Let An be the smallest positive integer satisfying An mod pi = i for all 1 ≤ i ≤ n, where pi is thei-th prime.
For example A2 = 5, since this is the smallest positive solution of the system of equations
For example A2 = 5, since this is the smallest positive solution of the system of equations
The system of equations for A3 adds another constraint. That is, A3 is the smallest positive solution of
and hence A3 = 23. Similarly, one gets A4 = 53 and A5 = 1523.
Let S(n) be the sum of all primes up to n that divide at least one element in the sequence A.
For example, S(50) = 69 = 5 + 23 + 41, since 5 divides A2, 23 divides A3 and 41 divides A10 = 5765999453. No other prime number up to 50 divides an element in A.
For example, S(50) = 69 = 5 + 23 + 41, since 5 divides A2, 23 divides A3 and 41 divides A10 = 5765999453. No other prime number up to 50 divides an element in A.
Find S(300000).