Souvik Dey

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

— Augustus De Morgan

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49 Questions

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11	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 $x$?
7	$f(x+y) + f( f(x) + f(y) ) = f( f( x+f(y) ) + f( y+f(x) ) )$
6	$\frac{a+b}{b+c} + \frac{c+d}{d+a} ≤ 4(\frac{a+c}{b+d}) ; a , b , c , d ∈ [1 , 2]$
6	Question about an upper bound
5	$\int_0^1 \sqrt {\tan^{-1}x}\space dx=$?

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1,230 Reputation

+15	Continuity of $f(x)=[x]+ \sqrt{x-[x]}$
+10	Integer Solutions to $x^2+y^2=5z^2$
+2	Proof that $P(A \mid C) = 1$ implies $P(A \mid B∩ C) = 1$
+5	$\int_0^1 \sqrt {\tan^{-1}x}\space dx=$?

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24 Answers

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6	$f(x+y) + f( f(x) + f(y) ) = f( f( x+f(y) ) + f( y+f(x) ) )$
5	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	Prove by mathematical induction for any prime number$ p > 3, p^2 - 1$ is divisible by $3$?

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54 Tags

8 functional-equations × 6	5 prime-twins
7 inequality × 12	4 sequences-and-series × 9
7 prime-numbers × 5	2 functions × 4
5 number-theory × 11	2 triangle × 3
5 algebra-precalculus × 3	2 euclidean-geometry × 2

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