Question

Let $\sum\limits_{n=1} ^{\infty} \frac{z^n}{1-z^n}$. Show that

score 146 · Answer 1 · 2026-04-26 00:52:25

146

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Let $\sum\limits_{n=1} ^{\infty} \frac{z^n}{1-z^n}$. Show that

Published on 26 Apr 2026 - 0:52

score 31 · Answer 2 · 2026-04-09 21:46:44

31

Views

Recursive Function value

Published on 09 Apr 2026 - 21:46

score 112 · Answer 3 · 2026-04-15 05:21:39

112

Views

Finding $f$ satisfies $\limsup_{n\to\infty}\frac{\tau(n)}{f(n)}=1$

Published on 15 Apr 2026 - 5:21

score 174 · Answer 4 · 2026-04-13 06:06:02

174

Views

sum of quadratic residues for $p=8k+7$

Published on 13 Apr 2026 - 6:06

score 59 · Answer 5 · 2026-04-15 14:09:22

For $ x,y,z $ positive real numbers satisfying 2$k^3$ + (x+y+z)$k^2$ - xyz = 0 where k is positive integer. Prove that xyz ≥ $(2k)^3$

score 88 · Answer 6 · 2026-05-05 17:51:24

88

Views

There are infinity many numbers when added to Three distinct integers making them pair-wise relatively prime

Published on 05 May 2026 - 17:51

score 426 · Answer 7 · 2026-04-30 13:56:21

426

Views

Calculating large Bell number modulo a composite number

Published on 30 Apr 2026 - 13:56

score 1.6k · Answer 8 · 2026-04-13 16:41:30

1.6k

Views

Sum equals the product

Published on 13 Apr 2026 - 16:41

score 47 · Answer 9 · 2026-04-13 21:26:33

47

Views

Fermat's last theorem of form a^b^c mod n

Published on 13 Apr 2026 - 21:26

score 161 · Answer 10 · 2026-05-05 17:53:41

161

Views

Which pairs of positive integers (,) satisfy $^2−2^=153$?

Published on 05 May 2026 - 17:53

score 91 · Answer 11 · 2026-04-16 05:28:53

91

Views

Find all primes p in the interval $[1, 4000]$, such that $2^{(p-1)}$ is congruent with $1\,\,(\mathrm{mod} \,\, p ^ 2)$.

Published on 16 Apr 2026 - 5:28

score 49 · Answer 12 · 2026-04-13 10:49:36

49

Views

General solutions/ Similar problems for the relationship between exponents and concatenation

Published on 13 Apr 2026 - 10:49

score 955 · Answer 13 · 2026-04-17 13:44:04

955

Views

Divisibility of $10^n-1$

Published on 17 Apr 2026 - 13:44

score 536 · Answer 14 · 2026-04-16 16:00:15

536

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Attempt to prove that (a,b) = (a,b,a+b)

Published on 16 Apr 2026 - 16:00

score 138 · Answer 15 · 2026-04-14 22:12:41

138

Views

Looking for a 1923 paper of Issai Schur on permutation polynomials

Published on 14 Apr 2026 - 22:12

List Question

Let $\sum\limits_{n=1} ^{\infty} \frac{z^n}{1-z^n}$. Show that

Recursive Function value

Finding $f$ satisfies $\limsup_{n\to\infty}\frac{\tau(n)}{f(n)}=1$

sum of quadratic residues for $p=8k+7$

For $ x,y,z $ positive real numbers satisfying 2$k^3$ + (x+y+z)$k^2$ - xyz = 0 where k is positive integer. Prove that xyz ≥ $(2k)^3$

There are infinity many numbers when added to Three distinct integers making them pair-wise relatively prime

Calculating large Bell number modulo a composite number

Sum equals the product

Fermat's last theorem of form a^b^c mod n

Which pairs of positive integers (,) satisfy $^2−2^=153$?

Find all primes p in the interval $[1, 4000]$, such that $2^{(p-1)}$ is congruent with $1\,\,(\mathrm{mod} \,\, p ^ 2)$.

General solutions/ Similar problems for the relationship between exponents and concatenation

Divisibility of $10^n-1$

Attempt to prove that (a,b) = (a,b,a+b)

Looking for a 1923 paper of Issai Schur on permutation polynomials

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