138 Why do both sine and cosine exist? 82 Produce an explicit bijection between rationals and naturals? 80 Why is there no “remainder” in multiplication 75 Why is an average of an average usually incorrect? 74 Best Fake Proofs? (A M.SE April Fools Day collection)

Reputation (132,621)

 +10 Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$ +10 How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$ +10 Proof that every common divisor of $a$ and $b$ is a divisor of $(a,b)$ without guessing the form of the GCD first +10 Main differences between analytic number theory and algebraic number theory

Questions (26)

 45 Functions $f:\mathbb{N}\rightarrow \mathbb{Z}$ such that $\left(m-n\right) \mid \left(f(m)-f(n)\right)$ 33 Prove $\frac{a^3+b^3+c^3}{3}\frac{a^7+b^7+c^7}{7} = \left(\frac{a^5+b^5+c^5}{5}\right)^2$ if $a+b+c=0$ 21 Name for a ring that also has composition - aka function application? 21 Is the numerator of $\sum_{k=0}^n \frac{(-1)^k}{2k+1}\binom{n}{k}$ a power of $2$? 17 Bézout's identity proof that if $(a,b,c)=1$ then $ax+bxy+cz=1$ has integer solutions

Tags (537)

 1k elementary-number-theory × 307 798 sequences-and-series × 222 1k calculus × 290 614 limits × 166 1k real-analysis × 269 606 combinatorics × 193 1k number-theory × 245 532 algebra-precalculus × 157 850 abstract-algebra × 235 403 integration × 95

Accounts (22)

 Mathematics 132,621 rep 13149301 Stack Overflow 1,099 rep 11026 English Language & Usage 191 rep 4 MathOverflow 179 rep 4 Database Administrators 156 rep 9