Use Euler's theorem to find a number (a) between 0 and 9 such that (a) is congruent

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Use Euler's theorem to find a number \(a\) between 0 and 9 such that \(a\) is congruent to \(7^{1000}\) modulo 10. (Note: This is the same as the last digit of the decimal expansion of \(7^{1000}\).)

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