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  • Member for 6 years, 8 months
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8 votes
1 answer
562 views

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

7 votes
1 answer
350 views

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

7 votes
0 answers
148 views

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

7 votes
4 answers
14k views

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

6 votes
2 answers
51 views

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

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

5 votes
3 answers
224 views

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

5 votes
1 answer
1k views

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

4 votes
1 answer
261 views

Number Theory Positive Divisor Problems

3 votes
2 answers
2k views

Number Theory Prime Reciprocals never an integer

3 votes
2 answers
292 views

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

3 votes
3 answers
368 views

Number Theory: Problems with Integer Squares

3 votes
3 answers
266 views

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

3 votes
1 answer
191 views

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

3 votes
1 answer
76 views

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

3 votes
2 answers
100 views

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

3 votes
4 answers
1k views

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

2 votes
2 answers
221 views

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

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.

2 votes
2 answers
36 views

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

2 votes
1 answer
219 views

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

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]

2 votes
2 answers
2k views

Number Theory: Complete set of residues modulo $n$

1 vote
1 answer
174 views

Number Theory: Mod Simultaneous Congruences

1 vote
1 answer
846 views

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

1 vote
2 answers
2k views

Number Theory Homework: Find 3 consecutive integers...

1 vote
0 answers
228 views

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

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]

1 vote
0 answers
426 views

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

0 votes
2 answers
31 views

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