User MathQuestion

8 votes

1 answer

562 views

How to show $p_n < p_1 + p_2 + \cdots + p_{n-1}$?

asked Sep 25, 2015 at 18:24

7 votes

1 answer

350 views

Number Theory: $x^2\equiv 1\pmod{140}$

number-theory elementary-number-theory modular-arithmetic quadratics congruences

asked Oct 13, 2015 at 1:05

7 votes

0 answers

148 views

Number Theory: $\binom{p-1}{k} \equiv (-1)^k \pmod{p}$

number-theory proof-verification prime-numbers modular-arithmetic binomial-coefficients

asked Oct 20, 2015 at 0:56

7 votes

4 answers

14k views

Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$

elementary-number-theory prime-numbers totient-function

asked Nov 1, 2015 at 6:59

6 votes

2 answers

51 views

Number Theory: Reordering $c_1,\dotsc,c_{10}$ so that $(2k-1)\mid(a_k-b_k)$

number-theory elementary-number-theory modular-arithmetic divisibility

asked Dec 7, 2015 at 23:36

5 votes

1 answer

2k views

Number Theory: Prove that $x^{p-2}+\dots+x^2+x+1\equiv 0\pmod{p}$ has exactly $p-2$ solutions

elementary-number-theory polynomials proof-verification prime-numbers modular-arithmetic

asked Nov 3, 2015 at 5:47

5 votes

3 answers

224 views

Number Theory: Find $m\equiv 1\pmod4$ so that $x^2\equiv -1\pmod{m}$ has no solution.

number-theory elementary-number-theory prime-numbers modular-arithmetic legendre-symbol

asked Dec 7, 2015 at 23:26

5 votes

1 answer

1k views

Number Theory: Chinese Remainder Theorem $x^2\equiv x\pmod{180}$

number-theory elementary-number-theory modular-arithmetic congruences chinese-remainder-theorem

asked Oct 13, 2015 at 23:54

4 votes

1 answer

261 views

Number Theory Positive Divisor Problems

number-theory elementary-number-theory prime-numbers divisibility prime-factorization

asked Sep 24, 2015 at 23:37

3 votes

2 answers

2k views

Number Theory Prime Reciprocals never an integer

number-theory elementary-number-theory prime-numbers divisibility prime-factorization

asked Sep 25, 2015 at 3:54

3 votes

2 answers

292 views

Number Theory: Prove there are infinitely many primes $p$ satisfying $n\mid (p-1)$

number-theory elementary-number-theory prime-numbers divisibility prime-factorization

asked Sep 22, 2015 at 4:04

3 votes

3 answers

368 views

Number Theory: Problems with Integer Squares

number-theory elementary-number-theory prime-numbers modular-arithmetic prime-factorization

asked Oct 25, 2015 at 18:20

3 votes

3 answers

266 views

Number Theory: Which numbers 101010...0101 are prime

number-theory elementary-number-theory prime-numbers

asked Oct 2, 2015 at 7:57

3 votes

1 answer

191 views

Number Theory: Prove that for any $n\exists k$ such that $n\mid\phi(k)$.

elementary-number-theory proof-verification prime-numbers totient-function

asked Nov 2, 2015 at 5:50

3 votes

1 answer

76 views

Number Theory: Show that $o_n(b)=m$ if $o_n(a)=m$ and $ab\equiv 1\pmod{n}$

number-theory elementary-number-theory proof-verification modular-arithmetic

asked Nov 2, 2015 at 3:13

3 votes

2 answers

100 views

Number Theory: Show that $10^{3^n}\equiv 1\pmod{3^{n+2}}$ but $3^{n+3}\not\mid 10^{3^n}-1$

number-theory elementary-number-theory proof-verification modular-arithmetic divisibility

asked Dec 8, 2015 at 0:38

3 votes

4 answers

1k views

Find all incongruent solutions of $x^8\equiv3\pmod{13}$.

number-theory elementary-number-theory prime-numbers modular-arithmetic primitive-roots

asked Dec 8, 2015 at 7:48

2 votes

2 answers

221 views

Number Theory: If $d\mid(4^n+1)$, show that $d$ is a sum of two squares

number-theory elementary-number-theory proof-verification prime-numbers modular-arithmetic

asked Dec 9, 2015 at 6:40

2 votes

3 answers

99 views

Prove that $\sum^{\infty}_{n=1}\frac{1}{n}\left(\frac{1+i}{\sqrt2}\right)^n$ converges but does not absolutely converge.

sequences-and-series complex-analysis convergence-divergence complex-numbers

asked Jan 29, 2016 at 7:27

2 votes

2 answers

36 views

Number Theory: Show that $o_n(a)=m$ odd implies $o_n(-a)=2m$.

number-theory elementary-number-theory prime-numbers modular-arithmetic

asked Nov 2, 2015 at 4:38

2 votes

1 answer

219 views

Number Theory: If $p\equiv 3\pmod{4}$, then $-r$ has order $(p-1)/2$ modulo $p$.

number-theory elementary-number-theory modular-arithmetic primitive-roots

asked Nov 3, 2015 at 23:00

2 votes

0 answers

3k views

Number Theory Prove $\gcd(a, b, c)=\gcd(\gcd(a,b),c)=\gcd(\gcd(a,c),b)=\gcd(\gcd(b,c),a)$. [duplicate]

number-theory elementary-number-theory gcd-and-lcm

asked Sep 15, 2015 at 22:02

2 votes

2 answers

2k views

Number Theory: Complete set of residues modulo $n$

elementary-number-theory modular-arithmetic congruences

asked Oct 2, 2015 at 6:43

1 vote

1 answer

174 views

Number Theory: Mod Simultaneous Congruences

number-theory elementary-number-theory modular-arithmetic

asked Oct 8, 2015 at 23:36

1 vote

1 answer

846 views

Number Theory: How to solve $x^2\equiv 4\pmod{143}$?

number-theory elementary-number-theory modular-arithmetic

asked Oct 13, 2015 at 21:54

1 vote

2 answers

2k views

Number Theory Homework: Find 3 consecutive integers...

number-theory elementary-number-theory modular-arithmetic divisibility congruences

asked Oct 14, 2015 at 6:04

1 vote

0 answers

228 views

Number Theory: Prove $x^k\equiv a\pmod{p}$ is solvable for $r^d,r^{2d},\dots,r^{[(p-1)/d]d}$.

number-theory elementary-number-theory proof-verification modular-arithmetic primitive-roots

asked Nov 19, 2015 at 7:48

1 vote

1 answer

949 views

Number Theory: Prove that any primitive root $r$ of $p^n$ is also a primitive root of $p$ [duplicate]

number-theory elementary-number-theory proof-verification modular-arithmetic primitive-roots

asked Nov 19, 2015 at 22:16

1 vote

0 answers

426 views

Number Theory: Find a primitive root of $13^{901}$ and find a complete set of primitive roots of $13$

number-theory elementary-number-theory modular-arithmetic totient-function primitive-roots

asked Dec 8, 2015 at 6:15

0 votes

2 answers

31 views

Visual representation of $\textrm{Re}(kz+m)>0$, with $k,m,z$ complex?

complex-numbers real-numbers

asked Jan 13, 2016 at 3:55

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35 Questions

How to show $p_n < p_1 + p_2 + \cdots + p_{n-1}$?

Number Theory: $x^2\equiv 1\pmod{140}$

Number Theory: $\binom{p-1}{k} \equiv (-1)^k \pmod{p}$

Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$

Number Theory: Reordering $c_1,\dotsc,c_{10}$ so that $(2k-1)\mid(a_k-b_k)$

Number Theory: Prove that $x^{p-2}+\dots+x^2+x+1\equiv 0\pmod{p}$ has exactly $p-2$ solutions

Number Theory: Find $m\equiv 1\pmod4$ so that $x^2\equiv -1\pmod{m}$ has no solution.

Number Theory: Chinese Remainder Theorem $x^2\equiv x\pmod{180}$

Number Theory Positive Divisor Problems

Number Theory Prime Reciprocals never an integer

Number Theory: Prove there are infinitely many primes $p$ satisfying $n\mid (p-1)$

Number Theory: Problems with Integer Squares

Number Theory: Which numbers 101010...0101 are prime

Number Theory: Prove that for any $n\exists k$ such that $n\mid\phi(k)$.

Number Theory: Show that $o_n(b)=m$ if $o_n(a)=m$ and $ab\equiv 1\pmod{n}$

Number Theory: Show that $10^{3^n}\equiv 1\pmod{3^{n+2}}$ but $3^{n+3}\not\mid 10^{3^n}-1$

Find all incongruent solutions of $x^8\equiv3\pmod{13}$.

Number Theory: If $d\mid(4^n+1)$, show that $d$ is a sum of two squares

Prove that $\sum^{\infty}_{n=1}\frac{1}{n}\left(\frac{1+i}{\sqrt2}\right)^n$ converges but does not absolutely converge.

Number Theory: Show that $o_n(a)=m$ odd implies $o_n(-a)=2m$.

Number Theory: If $p\equiv 3\pmod{4}$, then $-r$ has order $(p-1)/2$ modulo $p$.

Number Theory Prove $\gcd(a, b, c)=\gcd(\gcd(a,b),c)=\gcd(\gcd(a,c),b)=\gcd(\gcd(b,c),a)$. [duplicate]

Number Theory: Complete set of residues modulo $n$

Number Theory: Mod Simultaneous Congruences

Number Theory: How to solve $x^2\equiv 4\pmod{143}$?

Number Theory Homework: Find 3 consecutive integers...

Number Theory: Prove $x^k\equiv a\pmod{p}$ is solvable for $r^d,r^{2d},\dots,r^{[(p-1)/d]d}$.

Number Theory: Prove that any primitive root $r$ of $p^n$ is also a primitive root of $p$ [duplicate]

Number Theory: Find a primitive root of $13^{901}$ and find a complete set of primitive roots of $13$

Visual representation of $\textrm{Re}(kz+m)>0$, with $k,m,z$ complex?