# mathemagician

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 14 Of any 52 integers, two can be found whose difference of squares is divisible by 100 8 Why is the empty set a subset of every set? 7 Inequality on the side lengths of a triangle: $\left| \frac{a}{b} + \frac{b}{c} + \frac{c}{a} - \frac{a}{c} - \frac{b}{a} - \frac{c}{b} \right| < 1$. 7 Show $15x^{2} - 7y^{2} = 9$ has no integer solutions 6 Deduce that there exists a prime $p$ where $p$ divides $x^2 +2$ and $p≡3$ (mod 4)

# 2,130 Reputation

 +15 Does the sequence $f\chi_{E_n^c}$ converge pointwise to $f$ if the measure of $E_n$ tends to zero? -2 Inequality on the side lengths of a triangle: $\left| \frac{a}{b} + \frac{b}{c} + \frac{c}{a} - \frac{a}{c} - \frac{b}{a} - \frac{c}{b} \right| < 1$. +5 Convergence in Distribution +5 Question about covering spaces extending inverse.

# 32 Questions

 4 Problem involving Lebesgue Integral 3 Does the sequence $f\chi_{E_n^c}$ converge pointwise to $f$ if the measure of $E_n$ tends to zero? 3 Supremum equal limit of sequence of integrals 2 If functions converge a.e. and their integrals converge, does convergence in $L^1$ follow? 2 How to show function is measurable if and only if each component is

# 74 Tags

 21 elementary-number-theory × 9 14 pigeonhole-principle 17 real-analysis × 25 14 chinese-remainder-theorem 17 discrete-mathematics × 2 12 inequality × 3 15 geometry × 5 10 calculus × 6 14 elementary-set-theory × 3 10 proof-writing × 4

# 3 Accounts

 Mathematics 2,130 rep 415 Stack Overflow 108 rep 3 Cross Validated 103 rep 2