Question

Prove $F(x, y) = \sum_{i=1}^{p-1} x^i y^{p-i} \equiv 0 \mod p$, for $x \ne y$ and prime $p$

score 23 · Answer 1 · 2026-04-16 23:17:11

Prove $F(x, y) = \sum_{i=1}^{p-1} x^i y^{p-i} \equiv 0 \mod p$, for $x \ne y$ and prime $p$

Published on 16 Apr 2026 - 23:17

score 505 · Answer 2 · 2026-04-14 16:07:41

Find the formula for calculating the number of integers congruent to n mod p between a and b inclusive where a,b are integers

score 39 · Answer 3 · 2026-04-16 12:50:09

39

Views

How to find the congruence relation for the summation $\sum_{\substack{m<n_1<\cdots<n_r<p \\ n_i \equiv i \pmod 2}}\frac{1}{n_1\ldots n_r}$

Published on 16 Apr 2026 - 12:50

score 125 · Answer 4 · 2026-04-11 09:31:59

125

Views

Is the group of units of a ring an additive group?

Published on 11 Apr 2026 - 9:31

score 58 · Answer 5 · 2026-04-12 04:11:14

58

Views

Modular Equation Transformed as Matrix?

Published on 12 Apr 2026 - 4:11

score 168 · Answer 6 · 2026-04-11 17:15:45

168

Views

How many involutions does $\Bbb Z/999$ have?

Published on 11 Apr 2026 - 17:15

score 155 · Answer 7 · 2026-04-20 06:57:51

155

Views

How to find the general integer solution to an equation involving modulo with an unknown exponent?

Published on 20 Apr 2026 - 6:57

score 351 · Answer 8 · 2026-04-15 17:43:35

351

Views

Element of a cyclic group of even order has two square roots?

Published on 15 Apr 2026 - 17:43

score 45 · Answer 9 · 2026-04-15 15:22:04

45

Views

Distinguishing quadratic residues of a number

Published on 15 Apr 2026 - 15:22

score 207 · Answer 10 · 2026-04-17 15:20:31

207

Views

$\sum_{n=1}^{p-1}{\frac{1}{n}} = \frac{A_p}{B_p}$ What is $A_p$ (mod $p^2$) where $\frac{A_p}{B_p}$ is a reduced form fraction?

Published on 17 Apr 2026 - 15:20

score 244 · Answer 11 · 2026-04-18 05:37:45

244

Views

Find $x$ such that $x^{677} ≡ 3 \mod 2020$.

Published on 18 Apr 2026 - 5:37

score 23 · Answer 12 · 2026-04-12 16:31:43

23

Views

Solving two simultaneous modular equations for a maximum case solution

Published on 12 Apr 2026 - 16:31

score 44 · Answer 13 · 2026-04-15 17:12:31

44

Views

Calculate the remainder of $11^{2020} / 7$

Published on 15 Apr 2026 - 17:12

score 305 · Answer 14 · 2026-04-16 03:20:35

305

Views

How to solve $x^5\equiv 3 \pmod{19}$?

Published on 16 Apr 2026 - 3:20

score 344 · Answer 15 · 2026-04-17 02:59:26

344

Views

Smallest Number $k \in \mathbb{N}$ Such That $(2k-9)! \equiv 0\pmod{k!^2}$

Published on 17 Apr 2026 - 2:59

List Question

Prove $F(x, y) = \sum_{i=1}^{p-1} x^i y^{p-i} \equiv 0 \mod p$, for $x \ne y$ and prime $p$

Find the formula for calculating the number of integers congruent to n mod p between a and b inclusive where a,b are integers

How to find the congruence relation for the summation $\sum_{\substack{m<n_1<\cdots<n_r<p \\ n_i \equiv i \pmod 2}}\frac{1}{n_1\ldots n_r}$

Is the group of units of a ring an additive group?

Modular Equation Transformed as Matrix?

How many involutions does $\Bbb Z/999$ have?

How to find the general integer solution to an equation involving modulo with an unknown exponent?

Element of a cyclic group of even order has two square roots?

Distinguishing quadratic residues of a number

$\sum_{n=1}^{p-1}{\frac{1}{n}} = \frac{A_p}{B_p}$ What is $A_p$ (mod $p^2$) where $\frac{A_p}{B_p}$ is a reduced form fraction?

Find $x$ such that $x^{677} ≡ 3 \mod 2020$.

Solving two simultaneous modular equations for a maximum case solution

Calculate the remainder of $11^{2020} / 7$

How to solve $x^5\equiv 3 \pmod{19}$?

Smallest Number $k \in \mathbb{N}$ Such That $(2k-9)! \equiv 0\pmod{k!^2}$

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