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International competition SRMC 2005 P-1

Source:

September 7, 2010
number theory proposednumber theory

Problem Statement

Let n≥2n \geq 2 be natural number. Prove, that (1n−1+2n−1+....+(n−1)n−1)+1(1^{n-1}+2^{n-1}+....+(n-1)^{n-1})+1 divided by nn iff for any prime divisor pp of nn p∣np−1p| \frac{n}{p}-1 and (p−1)∣np−1(p-1)| \frac{n}{p}-1.
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