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Problem #PRU-21989

Problems Number Theory Divisibility Division with remainders. Arithmetic of remainders Arithmetic of remainders Numeral systems Decimal number system Euler's theorem Methods Pigeonhole principle Pigeonhole principle (other)

Prove that there is a power of 3 that ends in 001.

Problem #PRU-31235

Problems Number Theory Divisibility Division with remainders. Arithmetic of remainders Arithmetic of remainders

Find the last digit of the number \(1 \times 2 + 2 \times 3 + \dots + 999 \times 1000\).