### Questions (98)

 22 Confusing probability question 15 ${\gcd(n,m)\over n}{n\choose m}$ is an integer 14 When does $(p-1)! + 1 = p^k$ hold? [duplicate] 13 Exponential lower bound for the determiant of a (0,1)-matrix 12 What is the correct solution for the limit $\lim_{x\to\infty} x \sin\frac1x$?

### Reputation (2,850)

 +5 ${\gcd(n,m)\over n}{n\choose m}$ is an integer +10 Why this function is Riemann integrable? +5 Why isn't $\mathbb{Z} \to \mathbb{Q}$ surjective in the category of Rings? +5 Proving that the sum and difference of two squares (not equal to zero) can't both be squares.

### Answers (67)

 8 Number of 5 digit numbers $< 40,000$ 6 Evaluate $\lim_{x\to\infty}\left(1+\frac 4x\right)^{\frac x8}$ 5 Finding the maximum value of $\frac{5}{4x^{2}-16x+21}$ 4 Probability of a probability to happen 4 Proof that intervals of the form $[x, x+1)$ or $(x, x+1]$ must contain a integer.

### Tags (90)

 20 combinatorics × 10 8 graph-theory × 14 19 probability × 16 8 statistics × 12 15 discrete-mathematics × 5 8 calculus × 8 12 algebra-precalculus × 6 8 linear-algebra × 5 11 elementary-number-theory × 12 8 permutations × 2

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