jordan
Reputation
1,389
Next privilege 2,000 Rep.
2 18
Impact
~10k people reached

 5 Find the value of $a$, $b$ and $c$ for the given limit. 5 Show $x^2+4x+18\equiv 0\pmod{49}$ has no solution 5 Show $7!^{1/7} < 8!^{1/8}$ 5 Is the number $333{,}333{,}333{,}333{,}333{,}333{,}333{,}333{,}334$ a perfect square? 4 Check the convergence of $a_{n+1}=\sqrt{a_n+\frac{4}{a_n}}$ where $a_1=4$

### Reputation (1,389)

 +20 $\lfloor x^k \rfloor \equiv m \pmod{n}$ with $x$ irrational +15 Non-additive asymptotic upper density: $\mathsf{d}^\star(A\cup B) \neq \mathsf{d}^\star(A)+\mathsf{d}^\star(B)$ +15 $\liminf_n a_n = \inf_n a_n$ if $a_n \ge a_m$ when $n\mid m$ -2 How many integers $\{xy \colon 1\le x\le y\le 2x\}$?

### Questions (27)

 20 Finding all integer solutions of $5^x+7^y=2^z$ 7 How many integers $\{xy \colon 1\le x\le y\le 2x\}$? 6 Only finitely many $a, b$ such that $2+3^n+5^{n^2}=2^a7^b$ for some $n$? 6 The maximum of $\binom{n}{x+1}-\binom{n}{x}$ 4 $\lfloor x^k \rfloor \equiv m \pmod{n}$ with $x$ irrational

### Tags (68)

 24 elementary-number-theory × 27 8 sequences-and-series × 7 13 number-theory × 26 8 combinatorics × 6 13 calculus × 6 8 proof-strategy × 6 12 limits × 6 8 discrete-mathematics × 4 9 real-analysis × 7 8 divisibility × 3

### Accounts (3)

 Mathematics 1,389 rep 218 MathOverflow 195 rep 8 Quantitative Finance 101 rep