Question

find $f(99)$ where $2f(x-\frac{1}{x}) + f(\frac{1}{x}-x) = 3(x+\frac{1}{x})^2.$

score 119 · Answer 1 · 2026-04-17 12:25:32

119

Views

find $f(99)$ where $2f(x-\frac{1}{x}) + f(\frac{1}{x}-x) = 3(x+\frac{1}{x})^2.$

Published on 17 Apr 2026 - 12:25

score 49 · Answer 2 · 2026-05-10 23:39:30

49

Views

Prove or refute that $\sum_{n=1}^\infty\frac{1}{n^2+A\varphi(n)+B}$ will be irrational for some choice of integers $A,B\geq 1$

Published on 10 May 2026 - 23:39

score 504 · Answer 3 · 2026-04-15 03:55:37

504

Views

Why does the law of distributivity use the distributive property to prove it exists?

Published on 15 Apr 2026 - 3:55

score 199 · Answer 4 · 2026-04-13 23:18:30

199

Views

Is any subsequence of a sequence of rational numbers dense in $\mathbb{R}$

Published on 13 Apr 2026 - 23:18

score 1.9k · Answer 5 · 2026-05-10 20:52:34

1.9k

Views

Does there exist non trivial group homomorphism from $S_3$ to ( $\mathbb Q $,+)

Published on 10 May 2026 - 20:52

score 4.2k · Answer 6 · 2026-04-09 03:29:54

4.2k

Views

How to explain irrational numbers to laymen?

Published on 09 Apr 2026 - 3:29

score 1k · Answer 7 · 2026-04-15 08:40:26

1k

Views

Is there any continuous function that is only differentiable on $\mathbb{Q}$?

Published on 15 Apr 2026 - 8:40

score 106 · Answer 8 · 2026-04-15 17:37:47

106

Views

(Dis)continuity of $f(x)=\sum_{j: q_j < x} 2^{-j}$

Published on 15 Apr 2026 - 17:37

score 266 · Answer 9 · 2026-04-16 03:29:21

266

Views

find all rational points on $x^2+7 y^2 = 1$

Published on 16 Apr 2026 - 3:29

score 62 · Answer 10 · 2026-05-10 13:51:03

Is there a way to form a sequence of intervals s.t they cover all the rational numbers in $(0,1)$ in a way that $C_n \subset Int(C_{n+1}),$

score 314 · Answer 11 · 2026-05-10 15:51:21

314

Views

Irrationality of the Euler–Mascheroni constant

Published on 10 May 2026 - 15:51

score 238 · Answer 12 · 2026-04-15 20:54:37

238

Views

$n$ as an integer and a real number

Published on 15 Apr 2026 - 20:54

score 42 · Answer 13 · 2026-05-10 18:03:30

42

Views

Need the name of algebraic structure suitable for this

Published on 10 May 2026 - 18:03

score 70 · Answer 14 · 2026-05-11 01:14:36

70

Views

Equalities of a rational numbers

Published on 11 May 2026 - 1:14

score 175 · Answer 15 · 2026-04-17 10:13:55

175

Views

Proof Irrational number $x$, given $N\in{\mathbb{N}}$ exists $\epsilon>0$ so all rationals $\in{V_\epsilon{(x)}}$ have denominator larger than N.

Published on 17 Apr 2026 - 10:13

List Question

find $f(99)$ where $2f(x-\frac{1}{x}) + f(\frac{1}{x}-x) = 3(x+\frac{1}{x})^2.$

Prove or refute that $\sum_{n=1}^\infty\frac{1}{n^2+A\varphi(n)+B}$ will be irrational for some choice of integers $A,B\geq 1$

Why does the law of distributivity use the distributive property to prove it exists?

Is any subsequence of a sequence of rational numbers dense in $\mathbb{R}$

Does there exist non trivial group homomorphism from $S_3$ to ( $\mathbb Q $,+)

How to explain irrational numbers to laymen?

Is there any continuous function that is only differentiable on $\mathbb{Q}$?

(Dis)continuity of $f(x)=\sum_{j: q_j < x} 2^{-j}$

find all rational points on $x^2+7 y^2 = 1$

Is there a way to form a sequence of intervals s.t they cover all the rational numbers in $(0,1)$ in a way that $C_n \subset Int(C_{n+1}),$

Irrationality of the Euler–Mascheroni constant

$n$ as an integer and a real number

Need the name of algebraic structure suitable for this

Equalities of a rational numbers

Proof Irrational number $x$, given $N\in{\mathbb{N}}$ exists $\epsilon>0$ so all rationals $\in{V_\epsilon{(x)}}$ have denominator larger than N.

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