primitive roots: a survey
... depends on α, the limiting value of the fractional part of the base-2 logarithm of n. That is, it looks like lim n→∞ Pn does not exist! And this is indeed the case, though the oscillation in P n is very gentle. We have lim sup Pn ≈ 0.72135465 which is achieved when α ≈ 0.139, and lim inf Pn ≈ 0.7213 ...
... depends on α, the limiting value of the fractional part of the base-2 logarithm of n. That is, it looks like lim n→∞ Pn does not exist! And this is indeed the case, though the oscillation in P n is very gentle. We have lim sup Pn ≈ 0.72135465 which is achieved when α ≈ 0.139, and lim inf Pn ≈ 0.7213 ...
Build-Up Method Example. Find LCM(36,60).
... 5.2. COUNTING FACTORS, GREATEST COMMON FACTOR, AND LEAST COMMON MULTIPLE ...
... 5.2. COUNTING FACTORS, GREATEST COMMON FACTOR, AND LEAST COMMON MULTIPLE ...
6 Prime Numbers
... Theorem 6.17 If gcd (a, n) = 1 then the function ρa : Z∗n → Z∗n , [r]n 7→ [ar]n is a bijection. Proof The idea for the proof can be seen on p.259 and p.290. Is the function well-defined, i.e. does the image lie in Z∗n ? Assume [r]n ∈ Z∗n so gcd (r, n) = 1 by definition of Z∗n . By the assumption in ...
... Theorem 6.17 If gcd (a, n) = 1 then the function ρa : Z∗n → Z∗n , [r]n 7→ [ar]n is a bijection. Proof The idea for the proof can be seen on p.259 and p.290. Is the function well-defined, i.e. does the image lie in Z∗n ? Assume [r]n ∈ Z∗n so gcd (r, n) = 1 by definition of Z∗n . By the assumption in ...
