Kirthi Raman
• Member for 9 years, 7 months

 68 Funny identities 35 Which mathematicians have influenced you the most? 28 If $x$ and $y$ are rational numbers and $x^5+y^5=2x^2y^2,$ then $1-xy$ is a perfect square. 22 Numbers are too large to show $65^{64}+64^{65}$ is not a prime 21 What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$

### Reputation (7,268)

 +10 Integration: area enclosed by graph of $x^4 + y^4 = 1$ -2 Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$ +20 What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$ +10 What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$

### Questions (25)

 40 Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$ 14 Solve the integral $S_k = (-1)^k \int_0^1 (\log(\sin \pi x))^k dx$ 11 What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$ 7 Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers 7 Prove for any positive real numbers $a,b,c$ $\frac{a^3}{a^2+ab+b^2}+\frac{b^3}{b^2+bc+c^2}+\frac{c^3}{c^2+ca+a^2} \geq \frac{a+b+c}{3}$

### Tags (84)

 116 elementary-number-theory × 29 42 sequences-and-series × 10 91 integration × 21 35 polynomials × 5 72 calculus × 20 34 trigonometry × 11 63 algebra-precalculus × 13 34 inequality × 9 43 number-theory × 7 28 real-analysis × 7

### Bookmarks (39)

 1168 Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio? 293 Intuition for the definition of the Gamma function? 97 Why are all the interesting constants so small? [closed] 64 Does Fermat's Last Theorem hold for cyclotomic integers in $\mathbb{Q(\zeta_{37})}$? 40 Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$