[seqfan] The half-Giuga conjecture

[Tomasz Ordowski]

Dear SeqFans,

Let S(n) = Sum_{k=1..n-1} k^{(n-1)/2)} for an odd natural number n.

Conjecture: The congruence S(n) == +-1 (mod n) has no solution n > 1.

If there is a counterexample, it must be an absolute Euler pseudoprime.

Maybe someone will find counterexamples to this conjecture.

Best regards,

Thomas Ordowski
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http://mathworld.wolfram.com/GiugasConjecture.html
https://oeis.org/history/view?seq=A033181&v=75