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MathNet 2022-part-06 — 196 problems (EN–VI) Question 88

Math Olympiad Vault · MathNet 2022-part-06 — 196 problems (EN–VI)

Question 88

Compute the number of distinct pairs of the form
(first three digits of $x$, first three digits of $x^{4}$ )
over all integers $x\gt 10^{10}$.
For example, one such pair is $(100,100)$ when $x=10^{10^{10}}$.