Tuesday, April 26, 2011

σ(p^4)

The only prime p such that σ(p^4) is a square is 3.

σ(p^4) = 1 + p + p^2 + p^3 + p^4

when p = 3, 1 + 3 + 3^2 + 3^3 + 3^4 = 11^2

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