math problems and proofs combinatorics, number theory and geometry - b kisacanin

... class="bi x0 y0 w0 h0" alt=""

Ngày tải lên: 31/03/2014, 16:22

... class="bi x0 y0 w0 h0" alt=""

Ngày tải lên: 31/03/2014, 16:22

... other hand, bn-' + bn-2 + . . . + b2 + b + 1 consists of n digits all 1. Multiplying 11 1 - < /b> . 11 1 by the 1-digit number < /b> 6 - < /b> 1 gives ( 6- < /b> l) (b- l) (b- 1 )-( < /b> 6- < /b> l) (b- l) (b- I)(, ... 0-, < /b> I-, 2- < /b> or 3-power, mul- tiplied by 3 to the 0- < /b> or l-power, times 5 to the 0-, < /b> l- or 2-power, ti...

Ngày tải lên: 31/03/2014, 16:20

... 1–18 Multiplying by b, pub + abv = b. But now p | ab =⇒ p | b.  Now suppose a is neither a unit nor 0; and < /b> suppose that a is not expressible as a product of primes. Then a is reducible, by the Lemma above: ... b, pxb + aby = b. But p | pxb and < /b> p | aby (since p | ab). Hence p | b.  Theorem 1.3 Suppose n ∈ N, n > 0. Then n is expressible as a product of prime numb...

Ngày tải lên: 31/03/2014, 16:21

... A possibly equal to B) , and < /b> A  B means that A is a proper subset of B (i.e., A ⊆ B but A = B) . Further, A ∪ B denotes the union of A and < /b> B, A ∩ B the intersection of A and < /b> B, and < /b> A \ B the set ... dividing a by b. It is clear that b | a if and < /b> only if a mod b = 0. Dividing both sides of the equation a = bq + r by b, we obtain a /b...

Ngày tải lên: 03/04/2014, 12:23

... NONLINEAR OPTIMIZATION Theory < /b> and < /b> Examples JONATHAN M. BORWEIN Centre for Experimental and < /b> Constructive Mathematics Department of Mathematics and < /b> Statistics Simon Fraser University, Burnaby, B. C., Canada V5A 1S6 jborwein@cecm.sfu.ca http://www.cecm.sfu.ca/∼jborwein and < /b> ADRIAN ... has a number < /b> of advantages over always working in R n : the basis- i...

Ngày tải lên: 31/03/2014, 15:13

... a, b, and < /b> d be positive integers. Prove that if (a, b) =1andd divides a, then (d, b) =1. 10. Let a and < /b> b be positive integers. Prove that (a, b) =a if and < /b> only if a divides b. 11. Let a, b, c be ... (a 0 ,a 1 , ,a n ) and < /b> (b 0 ,b 1 , ,b n )inS such that the numbers a 0 ,a 1 , ,a n are rel- atively prime integers, the numbers b 0 ,b 1 , ,b n are r...

Ngày tải lên: 31/03/2014, 16:21

... a, 6, and < /b> s are positil'e integers, we write sb - < /b> 1 = Bb. sn - < /b> 1 = B, , P 18 Solved and < /b> Unsolved Problems < /b> in Number < /b> Theory < /b> Then if (a, b) = g, (Ba , Bb) = Bg L ... a1 - < /b> -_ < /b> - 1 Qn b qo +- < /b> 1 q1 + - < /b> q2 + -, < /b> and,< /b> specifically, Similarly from (e) a...

Ngày tải lên: 15/03/2014, 16:03