Question

Show that for $p$ prime, $\mathbb{Z}_p$ is the only finite field with cardinality $p$ (not counting Isomorphism)

score 45 · Answer 1 · 2026-04-14 00:56:50

45

Views

Show that for $p$ prime, $\mathbb{Z}_p$ is the only finite field with cardinality $p$ (not counting Isomorphism)

Published on 14 Apr 2026 - 0:56

score 68 · Answer 2 · 2026-04-15 07:59:12

68

Views

Determine the remainder we get if we divide $799^{801}$ by $264$

Published on 15 Apr 2026 - 7:59

score 1.3k · Answer 3 · 2026-04-08 19:29:25

1.3k

Views

Proving fraction is irreducible

Published on 08 Apr 2026 - 19:29

score 86 · Answer 4 · 2026-04-14 07:44:38

86

Views

Expected number of digits of the second-largest prime factor of a very large composite number?

Published on 14 Apr 2026 - 7:44

score 5.1k · Answer 5 · 2026-04-15 19:50:41

5.1k

Views

Prove $\gcd(n,n+2)=1$ if $n$ is odd and $2$ if $n$ is even

Published on 15 Apr 2026 - 19:50

score 87 · Answer 6 · 2026-04-13 23:01:59

87

Views

2 elementary number theory problems

Published on 13 Apr 2026 - 23:01

score 38 · Answer 7 · 2026-04-15 14:49:26

If $k, l, r, s \in \mathbb{Z^+} \text{ and } k^r=l^s$ prove that $l \text{ and } k$ are powers of some positive integer

score 105 · Answer 8 · 2026-04-17 05:31:43

105

Views

Relation between the numbers of units, square roots of unity and divisors for the rings $\mathbb{Z}/n\mathbb{Z}$

Published on 17 Apr 2026 - 5:31

score 684 · Answer 9 · 2026-05-10 16:10:15

684

Views

$x^2 \equiv -2,2 \pmod {122}$

Published on 10 May 2026 - 16:10

score 207 · Answer 10 · 2026-05-10 12:54:05

207

Views

if $19a^2 \equiv b^2 \pmod 7$ then $19a^2 \equiv b^2 \pmod {7^2}$

Published on 10 May 2026 - 12:54

score 385 · Answer 11 · 2026-04-14 00:39:40

385

Views

Proving the product of an odd number and the power of 2 is bijective

Published on 14 Apr 2026 - 0:39

score 104 · Answer 12 · 2026-04-16 06:12:43

104

Views

Find the smallest integer n such that the expression $40! \cdot 5^n$ has the maximum number of trailing zeros.

Published on 16 Apr 2026 - 6:12

score 105 · Answer 13 · 2026-04-13 18:39:04

105

Views

Why does this property hold for odd integers except for 5?

Published on 13 Apr 2026 - 18:39

score 484 · Answer 14 · 2026-05-11 05:29:05

484

Views

Find all Pythagorean triples $x^2+y^2=z^2$ where $x=21$

Published on 11 May 2026 - 5:29

score 1.3k · Answer 15 · 2026-04-12 02:37:53

1.3k

Views

Divisibilty vs. division, for negative divisors

Published on 12 Apr 2026 - 2:37

List Question

Show that for $p$ prime, $\mathbb{Z}_p$ is the only finite field with cardinality $p$ (not counting Isomorphism)

Determine the remainder we get if we divide $799^{801}$ by $264$

Proving fraction is irreducible

Expected number of digits of the second-largest prime factor of a very large composite number?

Prove $\gcd(n,n+2)=1$ if $n$ is odd and $2$ if $n$ is even

2 elementary number theory problems

If $k, l, r, s \in \mathbb{Z^+} \text{ and } k^r=l^s$ prove that $l \text{ and } k$ are powers of some positive integer

Relation between the numbers of units, square roots of unity and divisors for the rings $\mathbb{Z}/n\mathbb{Z}$

$x^2 \equiv -2,2 \pmod {122}$

if $19a^2 \equiv b^2 \pmod 7$ then $19a^2 \equiv b^2 \pmod {7^2}$

Proving the product of an odd number and the power of 2 is bijective

Find the smallest integer n such that the expression $40! \cdot 5^n$ has the maximum number of trailing zeros.

Why does this property hold for odd integers except for 5?

Find all Pythagorean triples $x^2+y^2=z^2$ where $x=21$

Divisibilty vs. division, for negative divisors

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