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Souvik Dey
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### Questions (277)

 21 Evaluate $\int_{0}^1 \prod_{k=2}^n \lfloor kx \rfloor dx$ 13 If $f:\mathbb{R}\to\mathbb{R}$ is continuous and $f(x)\neq x$ for all $x$, must it be true that $f(f(x))\neq x$ for all $x$? 12 Verifying the inequality $\sum_{i=1}^n \frac{\cos y_i}{\sin x_i}≤ \sum_{i=1}^n\cot x_i$ 11 $x,y,z$ positive real numbers , $x+y+z=3$ $\implies x^4y^4z^4(x^3+y^3+z^3)≤3$ 9 Partition of $\mathbb{R}^+$ into two semigroups

### Reputation (1)

 +5 If the normalizer of a subgroup in a group is equal to the subgroup then is the subgroup abelian? +5 For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ? +5 Pull back image of maximal ideal under surjective ring homomorphism is maximal +5 If $G$ is an uncountable group and $H$ is a subgroup then $G$ \ $H$ is uncountable ?

 7 $f(x+y) + f( f(x) + f(y) ) = f( f( x+f(y) ) + f( y+f(x) ) )$ 6 Primes and Twine primes and their sums. 4 Simple inequality on real numbers 4 Need hint: Determine whether the series $\sum_{n=1}^{\infty}(\frac{n}{n+1})^{n^2}$ is convergent or divergent. 2 3 never divides $n^2+1$

### Tags (117)

 9 functional-equations × 6 6 prime-twins 8 prime-numbers × 12 5 sequences-and-series × 26 7 number-theory × 39 4 elementary-number-theory × 7 7 inequality × 21 2 functions × 28 6 algebra-precalculus × 11 2 linear-algebra × 22

### Accounts (2)

 Physics 106 rep 2 Mathematics 1 rep 1739