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 13 Show that $x^{8}+5x^{2}=1$ has exactly $2$ real roots 8 Divergence for $p$ prime numbers and convergence for $m$ composite numbers 5 2013 USAMO problem 5 5 How many zeros are there at $1000!$ in the base $24$ 5 Prove $2\lfloor x\rfloor \le \lfloor2x\rfloor$

### Reputation (2,773)

 +35 If $\mathbb{RP}^n$ can be immersed in $\mathbb{R}^{n+1}$, how do I see that $n$ must be of the form $2^r - 1$ or $2^r - 2$? +20 Determinant of the following $(n\times n)$ matrix +15 How to proof that two lines in cube are perpendicular, without use of vectors +10 Finding the number of sequences with $0 \leq a_m \leq 3m$

### Questions (24)

 12 Coloring 5 Largest Numbers in Each Row and Column Yields at Least 25 Double-Colored Numbers 10 $l^\infty(I)$ and $l^\infty(J)$ isometrically isomorphic with $|I| \not= |J|.$ 5 Existence of Homomorphism so that Diagram Commutes 5 Expected Number of Steps to Order First n Integers 3 Multiple of $p$ in first $p+1$ Fibonacci Numbers

### Tags (80)

 32 real-analysis × 16 14 sequences-and-series × 5 27 calculus × 9 12 contest-math × 8 19 combinatorics × 13 12 discrete-mathematics × 7 16 algebra-precalculus × 5 11 elementary-number-theory × 7 14 linear-algebra × 9 11 convergence × 3

### Accounts (3)

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