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4

Part of 1964 German National Olympiad

Problems(1)

periodic are last digit of n^{(n^n)}

Source: 1963-64 Germany R4 12.4

10/12/2024
Denote by ana_n the last digit of the number n(nn)n^{(n^n)} (let n≠0n\ne 0 be a natural number ). Prove that the numbers ana_n form a periodic sequence and state this period!
number theorylast digitsDigitperiodic