i. m. soloveichik
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 48 Surprising identities / equations 9 If $a^3 b = ba^3$ and if $a$ has order 7, show that $ab = ba$ 8 Best book ever on Number Theory 7 Is the following field extension normal $\mathbb Q \sqrt {2+\sqrt 2}\mid \mathbb Q$ 7 Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.

### Reputation (3,226)

 +10 Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer. +10 Improper Rotations in Even Dimensions +10 Reduced Gröbner Basis +10 Finding the Fixed Fields in the Galois Correspondence for the Splitting Field of $x^4-3x^2+4$ over $\mathbb{Q}$

### Questions (9)

 9 Groups of order $n^2$ that have no subgroup of order $n$ 4 Unique normal subgroups of every possible order 4 Largest Equilateral Triangle in a Polygon 4 Another Presentation of Certain Cyclic Groups 4 Cyclic Group Presentation

### Tags (107)

 47 abstract-algebra × 31 17 elementary-number-theory × 12 43 group-theory × 33 15 calculus × 12 28 field-theory × 13 13 finite-groups × 16 22 linear-algebra × 13 12 algebra-precalculus × 17 20 galois-theory × 13 12 geometry × 14

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 Mathematics 3,226 rep 1718 MathOverflow 361 rep 211