# mathse

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"There are no facts, only interpretations."

"Last night I lay in bed looking up at the stars in the sky and I thought to myself, where the heck is the ceiling."

I have just noted that, oddly, this site has the same shorthand as myself: mathse (or Math.SE) ...

 7 CHECK: Let p be a prime number. Show that $\binom{2p}{p}$ is congruent to $2$ mod $p$. 6 How do I derive the formula for the sum of squares? 6 Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$ 6 Help with a Binomial Identity: $\sum_{k=0}^{\infty} \binom{n+k}{k}2^{-k} = 2^{n+1}$ 5 Proving two consecutive odd primes have at least 3 prime divisors.

# 1,817 Reputation

 +10 inequality $\prod\limits_{k=1}^n\frac{2k-1}{2k}\lt\frac1{\sqrt{3n}}$ +45 Compute Card$(\{(m_1,m_2,m_3)\in\{0,\cdots,75\}^3: m_1+m_2+m_3=75\})$. +2 Finding polynomials question (combinatorics) +10 CFG with reverse strings

# 7 Questions

 4 Math Olympiads: GCD of terms in a sequence equals GCD of terms in other sequence 2 binomial identity involving sum of diagonal elements 1 binomial coefficient divisibility properties 1 conditional expectation of square given sum of iid variables 0 When does $m$ divide $a^m$?

# 71 Tags

 25 combinatorics × 14 9 sequences-and-series × 5 21 proof-strategy × 8 7 proof-verification × 2 18 binomial-coefficients × 9 6 linear-algebra × 4 13 probability × 12 6 inequality × 3 11 elementary-number-theory × 9 5 probability-theory × 7

# 2 Accounts

 Mathematics 1,817 rep 112 MathOverflow 136 rep 4