Posted by **Steven** on Wednesday, July 24, 2013 at 5:46am.

Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence

Rx≡1(mod M)

if such an x exists. If such an x does not exist, put S(R,M)=0.

Each line of this text file contains a pair of space separated integers representing R and M, respectively.

Let L be the list of integers whose k-th element is the value of S(R,M), where R and M are taken from the k-th line of the text file.

Let T be the sum of all elements of L. What are the last three digits of T?

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