User alvoutila - Mathematics Stack Exchange

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	1,004 reputation	bio	website		visits	member for	2 years, 7 months
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2

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80

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How to show that $a^2+a+1 \equiv 0 \pmod p$?

homework elementary-number-theory

nov 7 '11 at 10:17 Jyrki Lahtonen 30.7k

2

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2

answers

204

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How to show that $n$ is a prime?

oct 4 '11 at 20:08 Charles 8,720

1

2

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2

answers

125

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show that $\gcd(a_1, \dots, a_n) = \gcd(a_1, \dots, a_{n-2},\gcd(a_{n-1},a_n))$

elementary-number-theory

sep 10 '11 at 22:51 Community♦ 1

1

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0

answers

36

views

Is always $\mathbb{D} \subset U$ in Poisson's integral formula?

complex-analysis integral

apr 6 at 21:56 Davide Giraudo 56.1k

1

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2

answers

29

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How to prove that if $f(z)$ is complex function, then $\Delta Re(f)=0=\Delta Im(f)$?

homework complex-analysis

apr 2 at 12:00 Gustavo Marra 1,642

1

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0

answers

20

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How to show by example that existence of boundary function of any set $U\subset \mathbb{C}$ is dependant of its set.

complex-analysis

mar 21 at 21:03 alvoutila 1,004

1

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1

answer

59

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How to compute $\int_C f'(z)/f(z) dz$, when $C$ is positively oriented disk $\{ z: |z|=4\}$, when $f(z)=\frac{(z-8)^2z^3}{(z-5)^4(z+2)^2(z-1)^5}$?

complex-analysis integration

feb 7 at 15:08 Ron Gordon 26.1k

1

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1

answer

43

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Is $B \setminus (A+x) = B \cap (A+x)^c = B \cap A^c + x$?

measure-theory

jan 28 at 18:52 leo 2,685

1

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0

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51

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Why outer measure is defined by $m_n^*(A)=\inf \bigg\{ \sum_{i=1}^\infty l(I_i):\mathbb{F}=\{I_1,I_2,… \}\mbox{ is Lebesgue cover of } A \bigg\} $?

measure-theory

jan 23 at 16:35 Sasha 41.4k

1

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2

answers

60

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How to show that absolute value of a complex number is invariant under complex conjugation?

complex-numbers

jan 19 at 11:19 Adi Dani 5,942

1

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3

answers

108

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How to find an example of matrix $A$ that satisfies $A^{-1} = \frac{1}{n} A$, where $A = [a_{ij}]_{n \times n}$?

matrices

nov 27 at 19:35 alvoutila 1,004

1

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2

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157

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Is following good way to define analytic function? What other better ways there are to define Analyticity of complex function?

complex-analysis

sep 14 at 8:38 Christian Blatter 32.3k

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4

answers

438

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How to use fundamental theorem of arithmetic to conclude that $\gcd(a^k,b^n)=1$ for all $k, n \in$ N whenever $a,b \in$ N with $\gcd(a,b)=1$?

homework elementary-number-theory

sep 12 at 3:46 Community♦ 1

1

vote

1

answer

113

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What is the difference between Complex derivative and Complex differentiability?

complex-analysis

aug 27 at 18:04 timur 6,216

1

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1

answer

103

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Why the contour integral of $f(z)=\frac{i-1}{z+i}$ is not zero although it should be because $f(z)$ is analytic?

complex-analysis

aug 25 at 13:07 DonAntonio 46.4k

1

vote

3

answers

75

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How you prove that $p^2 \mid m$ and $p^2 \mid n \Rightarrow p^2 \mid mn$?

elementary-number-theory

jun 17 '12 at 20:44 Cocopuffs 5,149

1

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1

answer

45

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Would you show how many different orders in this case is possible?

combinatorics

feb 13 '12 at 17:10 pedja 6,813

1

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0

answers

128

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How to show that $\hat{e}_m(k) = e^{-2 \pi mk/N}$ for all k?

homework linear-algebra

feb 1 '12 at 5:24 Michael Chen 1,864

1

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2

answers

408

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How do you get possible candidates for primitive roots of 12?

elementary-number-theory

dec 12 '11 at 15:53 Community♦ 1

1

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2

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57

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How to prove $k^n \equiv 1 \pmod {k-1}$ (by induction)?

elementary-number-theory induction

dec 6 '11 at 18:41 Martin Sleziak 20.3k

1

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1

answer

61

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How do you get Jacobi symbol $[\frac{3}{8}]$?

elementary-number-theory

dec 3 '11 at 10:54 Will Jagy 21.6k

1

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1

answer

87

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How to show that $p \nmid a \Rightarrow \gcd(p,a)=1$?

elementary-number-theory

nov 19 '11 at 18:38 Michael Hardy 47.9k

1

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2

answers

32

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How to show that $\bar{a}^t \equiv (\bar{a}^ta^t)(a^t)$?

homework elementary-number-theory

nov 6 '11 at 12:28 Brian M. Scott 154k

1

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1

answer

85

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Can one show that if $\gcd(p^k,b)=1$, then $p^k \nmid b$?

elementary-number-theory

oct 29 '11 at 20:19 Michael Hardy 47.9k

1

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1

answer

78

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How is following possible: $\gcd(a_{n-1}, a_n) \mid a_{n-1}$ and $\gcd(a_{n-1}, a_n) \mid a_n$?

homework elementary-number-theory

oct 28 '11 at 15:47 Zev Chonoles♦ 53.2k

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3

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196

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If $x^2+y^2=z^2$, why can't $x$ and $y$ both be odd?

homework elementary-number-theory

oct 25 '11 at 21:06 JavaMan 8,270

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2

answers

71

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How to show that xyz is even( 2|xyz), when $x+y=z$?

homework elementary-number-theory

oct 24 '11 at 18:03 alvoutila 1,004

1

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1

answer

95

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How to show that integers $x_0+\frac{m}{d}t$, $t = 0, 1,…, d-1$, are pairwise incongruent modulo m.(Hint! Antithesis.)?

homework elementary-number-theory

sep 21 '11 at 16:35 J. M. 38.9k

1

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1

answer

53

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How to show that $\hat{e}_m(k) = e^{−2πimk/N}$ for all $k$? How to show that $\hat{F}_m = e_m$?

linear-algebra

jan 9 '11 at 21:55 Mose Wintner 160

1

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3

answers

82

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How to prove: for any $m \in Z$, $\sum_{n=m}^{m+N-1} h(n) =\sum_{n=0}^{N-1} h(n)$

linear-algebra homework

nov 11 '10 at 13:58 Derek Jennings 9,260

alvoutila

126 Questions