query: Euler theorem in determining the residue
positive_passages.docid: 4972
positive_passages.text: Mod of numbers with large exponents [modular order reduction]
negative_passages.docid: 49938
negative_passages.text: Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
negative_passages.docid: 116778
negative_passages.text: Calculation of an integral via residue.
negative_passages.docid: 78379
negative_passages.text: Proof on cubic residues
negative_passages.docid: 49074
negative_passages.text: Compute $\int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx$ via residue calculus.
negative_passages.docid: 45958
negative_passages.text: Proof that the Euler characteristic is additive
negative_passages.docid: 4742
negative_passages.text: Find the poles and residue of the function $\frac{1}{z-\sin z }$ at $z=0$?
negative_passages.docid: 39276
negative_passages.text: Ground Plan - Prove Fermat-Euclid's Totient Theorem with Lagrange's Theorem
negative_passages.docid: 765
negative_passages.text: $\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
negative_passages.docid: 104904
negative_passages.text: Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.
negative_passages.docid: 77070
negative_passages.text: Prove Euler's Theorem when the integers are not relatively prime
negative_passages.docid: 65141
negative_passages.text: Simple proof Euler–Mascheroni $\gamma$ constant
negative_passages.docid: 140249
negative_passages.text: Euler Product formula for Riemann zeta function proof
negative_passages.docid: 52353
negative_passages.text: Bounding Euler's e by showing $2 \leq \left (1+ \frac{1}{n}\right)^n < 3$
negative_passages.docid: 157946
negative_passages.text: Elementary derivation of certian identites related to the Riemannian Zeta function and the Euler-Mascheroni Constant
negative_passages.docid: 47148
negative_passages.text: Complete balanced (signed) residue System of an odd modulo m
negative_passages.docid: 130300
negative_passages.text: Proof that every quadratic residue has two roots, modulo a prime