Saurabh
Reputation
1,940
Next privilege 2,000 Rep.
1 6 28
Impact
~55k people reached

 12 If $\gcd(a,35)=1$ then show that $a^{12} \equiv 1 \pmod{35}$ 8 Integral of $\int \sqrt{1-4x^2}$ 5 Limit of the sequence $\lim_{n\rightarrow\infty}\sqrt[n]n$ 5 Little help with some algebra 5 finding all integer $n$ such that $n\mid2^{n!}-1$

### Reputation (1,940)

 +10 Limit of the sequence $\lim_{n\rightarrow\infty}\sqrt[n]n$ +5 Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$ +5 Show that the product of the $\phi(p-1)$ primitive roots of $p$ is congruent modulo $p$ to $(-1)^{\phi(p-1)}$ +5 Using combinatorial argument prove that $\frac{(3n)!}{2^n\times 3^n}$ is an integer.

### Questions (23)

 8 If $\gcd(a,35)=1$ then show that $a^{12} \equiv 1 \pmod{35}$ 7 Can $a^2+b^2+2ac$ be a perfect square if $c\neq \pm b$? 7 Prove $\binom{p-1}{k} \equiv (-1)^k\pmod p$ 6 Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them 5 Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$

### Tags (44)

 29 elementary-number-theory × 21 9 integration × 2 13 geometry × 4 8 puzzle × 2 13 algebra-precalculus × 4 7 algorithms × 3 11 trigonometry × 3 7 triangle × 2 9 calculus × 2 7 sequences-and-series × 2

### Accounts (26)

 Mathematics 1,940 rep 1628 Computer Science 299 rep 412 Area 51 204 rep 5 Physics 148 rep 4 English Language & Usage 138 rep 5