E554 -- Disquitio accuratior circa residua ex divisione quadratorum altiorumque potestatum per numeros primos relicta

(A more exact disquisition about the residues remaining from the division of squares and of higher powers by prime numbers)


Euler opens by noting the symmetry in the sequence of quadratic residues, then covers some of the group theoretic properties. The material is similar to that in E242. In section 46, he starts to look at higher power residues. In section 48 he gets back to primitive roots.

According to the records, it was presented to the St. Petersburg Academy on May 18, 1772.

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