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Relatively prime integers

Description

Two integers \(a\) and \(b\) are said to be relatively prime if the only positive integer that divides both of them is 1.

The positive integers less than 10 which are relatively prime to 10 are:

1, 3, 7, 9

therefore the sum of positive integers less than 10 which are relatively prime is 20.


Question

What is the sum of all positive integers less than 1,000,000 which are relatively prime to 1,000,000?


What is the sum of all positive integers less than 1,000,000 which are relatively prime to 1,000,000?