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# Problem 531

Chinese leftovers

Let g(a,n,b,m) be the smallest non-negative solution x to the system:
x = a mod n
x = b mod m
if such a solution exists, otherwise 0.

E.g. g(2,4,4,6)=10, but g(3,4,4,6)=0.

Let φ(n) be Euler’s totient function.

Let f(n,m)=g(φ(n),n,φ(m),m).

Find ∑f(n,m) for 1000000 ≤ n < m < 1005000.

x = a mod n
x = b mod m