# Souvik Dey

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" The moving power of mathematical invention is not reasoning but imagination. "

— Augustus De Morgan

# 273 Questions

 20 Evaluate $\int_{0}^1 \prod_{k=2}^n \lfloor kx \rfloor dx$ 14 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 $x$? 13 Verifying the inequality $\sum_{i=1}^n \frac{\cos y_i}{\sin x_i}≤ \sum_{i=1}^n\cot x_i$ 12 $x,y,z$ positive real numbers , $x+y+z=3$ $\implies x^4y^4z^4(x^3+y^3+z^3)≤3$ 9 A divisibility question concerning positive integers

# 3,495 Reputation

 +5 Irrationality of $n$-th root of positive rationals other than $1$ +5 A good introductory book on Ring and Field theory with a view towards Number Theory ? +5 Does there exist unique $c \in (0,1)$ such that $f'(c)=f(c)$? +5 Does there exist a non-commutative ring of order $210$?

# 33 Answers

 8 $f(x+y) + f( f(x) + f(y) ) = f( f( x+f(y) ) + f( y+f(x) ) )$ 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. 3 $f: \Bbb N→ \Bbb N$ , $f\big(f(m) +f(n)\big)=m+n$ $\space$ for all $m,n∈\Bbb N$

# 117 Tags

 11 functional-equations × 6 7 algebra-precalculus × 11 9 sequences-and-series × 27 6 prime-twins 9 prime-numbers × 9 4 elementary-number-theory × 7 8 number-theory × 36 4 summation × 5 7 inequality × 21 3 functions × 28

# 2 Accounts

 Mathematics 3,495 rep 639 Physics 106 rep 2

# 33 Badges

 Custodian × 6 Yearling × 2 Caucus Promoter Benefactor Curious Explainer Inquisitive Autobiographer Nice Question × 7

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