# Siddhant Trivedi

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# 42 Questions

 14 A typical example of Homeomorphism 11 How to prove Lagrange trigonometric identity [duplicate] 6 Evaluate :$\int \frac{\sin^{-1} \sqrt{x} -\cos^{-1} \sqrt{x}}{\sin^{-1} \sqrt{x} +\cos^{-1} \sqrt{x}} dx$ 4 Examples of open set 4 Number of elements of a finite field [duplicate]

# 1,070 Reputation

 +73 A typical example of Homeomorphism +5 What are the subspaces in $P_2$? +10 Factoring numbers of the form $11111111$ +15 Prove that $G$ is the internal direct product of $H$ and $K$

 14 Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$. 7 Prove that $a_n = \{\left(1+\frac{1}{n}\right)^n\}$ is bounded sequence, $n\in\mathbb{N}$ 3 What is the remainder of dividing $14^{256}$ by $17$? 3 Show that $a^{\phi(b)}+b^{\phi(a)} \equiv 1 (\text{mod }ab)$ , if a and b are relatively prime positive integers. 2 $f(x)=e^{|x|+x^2} +|x^2-1|$ is differentiable at $0,-1,1,2$?

# 55 Tags

 18 abstract-algebra × 19 3 polynomials × 3 17 group-theory × 7 3 algebra-precalculus × 3 9 sequences-and-series × 4 3 congruences 7 elementary-number-theory × 9 2 exponentiation × 2 4 real-analysis × 9 1 limits × 8

# 8 Accounts

 Mathematics 1,070 rep 421 Meta Stack Exchange 101 rep Web Applications 101 rep TeX - LaTeX 101 rep English Language & Usage 101 rep