OF DIOPHANTINE APPROXIMATIONS
... is true if either p = 1 or v = 1. Hence we may assume 0 = /i< 1, 0 = v < 1. Pick two (not necessarily distinct) primes P = PieS1, Q = QseS2 from the sets (1.8). We now restrict our attention to p' = Pp, q' = Q". It suffices to show ...
... is true if either p = 1 or v = 1. Hence we may assume 0 = /i< 1, 0 = v < 1. Pick two (not necessarily distinct) primes P = PieS1, Q = QseS2 from the sets (1.8). We now restrict our attention to p' = Pp, q' = Q". It suffices to show ...
n - Smarandache Notions Journal
... Chapter 1: Smarandache Function applied to perfect numbers Chapter 2: A result obtained using the Smarandache Function Chapter 3: A Congruence with the Smarandache Function Chapter 4: A functional recurrence to obtain the prime numbers using the Smarandache prime function Chapter 5: The general term ...
... Chapter 1: Smarandache Function applied to perfect numbers Chapter 2: A result obtained using the Smarandache Function Chapter 3: A Congruence with the Smarandache Function Chapter 4: A functional recurrence to obtain the prime numbers using the Smarandache prime function Chapter 5: The general term ...
![arXiv:math/0008222v1 [math.CO] 30 Aug 2000](http://s1.studyres.com/store/data/015263483_1-3fbf9f2fcdc71976e9b3a5d7ef45a284-300x300.png)
Holt Algebra 2 5-2
... Example 2A: Graphing Quadratic Functions in Standard Form Consider the function f(x) = 2x2 – 4x + 5. e. Graph the function. Graph by sketching the axis of symmetry and then plotting the vertex and the intercept point (0, 5). Use the axis of symmetry to find another point on the parabola. Notice that ...
... Example 2A: Graphing Quadratic Functions in Standard Form Consider the function f(x) = 2x2 – 4x + 5. e. Graph the function. Graph by sketching the axis of symmetry and then plotting the vertex and the intercept point (0, 5). Use the axis of symmetry to find another point on the parabola. Notice that ...
Congruence Properties of the Function that Counts Compositions
... above fact show us that the sequence ϑ(n) is completely describable modulo 2N +1 as well. Further, note that Table 1 lists only those even and odd numbers n such that s2 (n + 2) ≤ 3. The recurrence (5) shows then that the corresponding table for ϑ(n) modulo 8 will list only those even numbers n such ...
... above fact show us that the sequence ϑ(n) is completely describable modulo 2N +1 as well. Further, note that Table 1 lists only those even and odd numbers n such that s2 (n + 2) ≤ 3. The recurrence (5) shows then that the corresponding table for ϑ(n) modulo 8 will list only those even numbers n such ...
Rational Functions
... zero from the right, the values of f (x) gets larger and larger, we say f (x) is unbounded in both direction ...
... zero from the right, the values of f (x) gets larger and larger, we say f (x) is unbounded in both direction ...
some remarks on number theory >t 6
... we obtain by a simple computation that for all n c l / loglog n < A(n, a) < c2 logloglog n . III Sivasankaranarayana, Pillai and Szekeres proved that for 1 < l _<_ 16 any sequence of l consecutive integers always contains one which is relatively prime to the others, but that this is in general not t ...
... we obtain by a simple computation that for all n c l / loglog n < A(n, a) < c2 logloglog n . III Sivasankaranarayana, Pillai and Szekeres proved that for 1 < l _<_ 16 any sequence of l consecutive integers always contains one which is relatively prime to the others, but that this is in general not t ...
AN ARITHMETIC FUNCTION ARISING FROM THE DEDEKIND ψ
... currently evades us. Numerical evidence seems to suggest that the elements of B (other than 1) are all primes, but we have no proof or counterexample. We may, however, prove the following fact quite easily. The analogue of the following theorem for Euler’s totient function was originally proven by C ...
... currently evades us. Numerical evidence seems to suggest that the elements of B (other than 1) are all primes, but we have no proof or counterexample. We may, however, prove the following fact quite easily. The analogue of the following theorem for Euler’s totient function was originally proven by C ...
infinite series
... ranked together with Newton and Gauss as one of the greatest scientists of all time. The modern study of infinite series began in the seventeenth century with Newton, Leibniz, and their contemporaries. The divergence of (called the harmonic series) was known to the medieval ...
... ranked together with Newton and Gauss as one of the greatest scientists of all time. The modern study of infinite series began in the seventeenth century with Newton, Leibniz, and their contemporaries. The divergence of (called the harmonic series) was known to the medieval ...
Full text
... We now set each term pe of Q equal to S(xn) and seek to find xn such that X = {xn}n>l is an increasing sequence of positive integers. For definiteness, we define xn to be the smallest positive integer such that xn > xw_1? beginning with x{ = 2. Using the result in (5), we may thus uniquely determine ...
... We now set each term pe of Q equal to S(xn) and seek to find xn such that X = {xn}n>l is an increasing sequence of positive integers. For definiteness, we define xn to be the smallest positive integer such that xn > xw_1? beginning with x{ = 2. Using the result in (5), we may thus uniquely determine ...