Sarastro
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1,598
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 37 $x$, $y$, $x+y$ and $x-y$ are prime numbers. What is their sum? 15 The minimum value of $a^2+b^2+c^2+\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}?$ 11 If $y=x^{x^{x^{x^{x^{.^{.^{.}}}}}}}$ then how $y=x^y$? 5 How do I prove that $\{AB-BA\}$ does not span matrix space? 4 How many ways can $2m$ be represented as the sum of 4 natural numbers $\le m$?

### Reputation (1,598)

 +10 Matrices - Conditions for $AB+BA=0$ +10 On the restriction of field homomorphisms to subfields +10 Show that $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in R[x]$ is nilpotent iff $a_0,a_1,a_2,\ldots,a_n$ are nilpotent +10 Proof Verification Regarding Image of $K$-homomorphisms of a Normal Extension

### Questions (4)

 18 Matrices - Conditions for $AB+BA=0$ 3 Forming a new matrix by adding the same number to any row or column 2 On the restriction of field homomorphisms to subfields 2 On the roots of $t^4-6\sqrt3t^3+8t^2+2\sqrt3t-1=0$

### Tags (45)

 43 elementary-number-theory × 3 11 limits 37 prime-numbers 11 infinity 37 summation 11 tetration 15 inequality 9 linear-algebra × 6 12 probability × 9 9 combinatorics × 3

### Accounts (7)

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