Texte intégral
HOMEWORK VII
on the material from lectures on Oct, 23 and partially Oct, 30 MATH-UA 0248-001 THEORY OF NUMBERS
due on Nov, 3, 2017 1. Determine all the primitive roots of the prime 17.
2. For a prime p > 3prove that the primitive roots of poccur in pairs r, r0 with rr0 ≡ 1 (mod p). (Hint: if r is a primitive root of p, consider the integer r0 =rp−2).
3. Show that 1000! terminates in 249 zeros.
4. Show that
N
X
n=1
µ(n)[N/n] = 1.
1
Documents relatifs
In Section 3 we give a new (very short) proof of the result of [M], using a theorem of Kolmogorov on conjugate functions (see Section 2 for definitions and properties of conjugate
These systems allows the following of the dynamics of early root development in a high throughput manner and will be probably very useful to screen the root architecture of rice core
Oeuvre d’Art par Aldo Cruces-Newhall MathsLibres.com vous shouhaite Joyeux Noël... Comptage de 12 Jours de Noël par 8 (A) Réponses Comptage de huit bonnes
Frage des Leseverständnisses, wo die Lerner solche Aufgaben während des Kurses nicht genug behandelt haben, könnte die Verbesserungsstunde für den Lehrer eine Gelegenheit den
That is why, rather than proposing a complete set of economic measures and plans, the emphasis here has been to ask questions of method and highlight three essential ingredients for
Soit f une fonction continue et positive sur [a; b] et F une primitive de f sur [a;
The Hobbesian conception of social contract or the assistance of the poor by the State On the contrary the Hobbesian conception of the social contract contains the idea of
This paper defines and studies the notion of primitive root of a bi-periodic infinite picture, that is a rectangular pattern that tiles the bi-periodic picture and contains exactly
