{"app":{"locale":"en-GB"},"problem":{"content":"

Let f(n) be the largest positive integer x less than 10⁹ such that the last 9 digits of n^x form the number x (including leading zeros), or zero if no such integer exists.

For example:

f(4) = 411728896 (4^411728896 = ...490411728896)
f(10) = 0
f(157) = 743757 (157⁷⁴³⁷⁵⁷ = ...567000743757)
∑ f(n), 2 ≤ n ≤ 10³ = 442530011399

Find ∑ f(n), 2 ≤ n ≤ 10⁶.

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