Question

Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$

score 192 · Answer 1 · 2026-04-13 17:17:24

192

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Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$

Published on 13 Apr 2026 - 17:17

score 49 · Answer 2 · 2026-04-16 23:29:51

49

Views

Show that $D=\{(x,y) \in R^2:-1<x<1,0<y<\sqrt{1-x^2}\}$ is open

Published on 16 Apr 2026 - 23:29

score 378 · Answer 3 · 2026-04-13 01:08:30

378

Views

Berge's Theorem of the Maximum for correspondences mapping into subsets of $L^1$

Published on 13 Apr 2026 - 1:08

score 126 · Answer 4 · 2026-04-13 13:16:31

126

Views

Proof that makes use of the differentiability of a function and of its convex conjugate

Published on 13 Apr 2026 - 13:16

score 96 · Answer 5 · 2026-04-14 16:12:47

96

Views

Proofs With Algebraic Axioms

Published on 14 Apr 2026 - 16:12

score 1.3k · Answer 6 · 2026-04-12 10:38:58

1.3k

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Proving that a function is not injective.

Published on 12 Apr 2026 - 10:38

score 208 · Answer 7 · 2026-04-15 14:02:45

208

Views

Disprove: There exist unique integers $q$ and $r$ such that $204=25q+r$.

Published on 15 Apr 2026 - 14:02

score 63 · Answer 8 · 2026-04-16 05:37:20

63

Views

Prove that if $a\mid(2b^2+5c^2)$, then $a\nmid(3b^2-2c^2)$ or $a\le{19c^2}$.

Published on 16 Apr 2026 - 5:37

score 68 · Answer 9 · 2026-04-16 06:44:40

68

Views

Show that $\sum_{k=1}^{p}{{p+1}\choose k}2^k=\sum_{k=1}^{p}{{p+1}\choose k}2^{p+1-k}$

Published on 16 Apr 2026 - 6:44

score 289 · Answer 10 · 2026-04-13 08:36:09

289

Views

Why do we need the commutative axiom of multiplication?

Published on 13 Apr 2026 - 8:36

score 186 · Answer 11 · 2026-04-12 14:14:21

186

Views

Equivalent definition of irreducible topological subspace.

Published on 12 Apr 2026 - 14:14

score 103 · Answer 12 · 2026-04-15 16:37:23

103

Views

Prove the following infinite trig product by induction.

Published on 15 Apr 2026 - 16:37

score 334 · Answer 13 · 2026-04-14 07:45:19

334

Views

Proof (not by counterexample) that $A$ and $B$ being independent given $C$ does not imply independence given $C^c$

Published on 14 Apr 2026 - 7:45

score 85 · Answer 14 · 2026-04-10 10:19:46

85

Views

Spectral theory: Operator compact implies existence of convergent subsequence

Published on 10 Apr 2026 - 10:19

score 1k · Answer 15 · 2026-04-16 14:12:39

1k

Views

Orthogonal matrix multiplied by diagonal matrix multiplied by transpose of the orthogonal matrix

Published on 16 Apr 2026 - 14:12

List Question

Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$

Show that $D=\{(x,y) \in R^2:-1<x<1,0<y<\sqrt{1-x^2}\}$ is open

Berge's Theorem of the Maximum for correspondences mapping into subsets of $L^1$

Proof that makes use of the differentiability of a function and of its convex conjugate

Proofs With Algebraic Axioms

Proving that a function is not injective.

Disprove: There exist unique integers $q$ and $r$ such that $204=25q+r$.

Prove that if $a\mid(2b^2+5c^2)$, then $a\nmid(3b^2-2c^2)$ or $a\le{19c^2}$.

Show that $\sum_{k=1}^{p}{{p+1}\choose k}2^k=\sum_{k=1}^{p}{{p+1}\choose k}2^{p+1-k}$

Why do we need the commutative axiom of multiplication?

Equivalent definition of irreducible topological subspace.

Prove the following infinite trig product by induction.

Proof (not by counterexample) that $A$ and $B$ being independent given $C$ does not imply independence given $C^c$

Spectral theory: Operator compact implies existence of convergent subsequence

Orthogonal matrix multiplied by diagonal matrix multiplied by transpose of the orthogonal matrix

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