Question

Find N such that for all x $\ge$ N, $P(x)$ is Divisible by Primes Bigger than 10

score 69 · Answer 1 · 2023-10-23 14:33:21

69

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Find N such that for all x $\ge$ N, $P(x)$ is Divisible by Primes Bigger than 10

Published on 23 Oct 2023 - 14:33

score 63 · Answer 2 · 2026-03-28 20:13:00

63

Views

Given $a,b \in \mathbb{N}$, is it true that $\phi(\gcd(a,b))=\gcd(\phi(a),\phi(b))$?

Published on 28 Mar 2026 - 20:13

score 54 · Answer 3 · 2023-10-23 22:04:44

54

Views

Prove that a*b is not divisible by prime number p

Published on 23 Oct 2023 - 22:04

score 72 · Answer 4 · 2023-10-23 22:27:42

72

Views

Formulas that generate "too few" primes

Published on 23 Oct 2023 - 22:27

score 46 · Answer 5 · 2026-02-23 10:18:40

46

Views

Why do all parasitic numbers seem to be multiples of repunits?

Published on 23 Feb 2026 - 10:18

score 121 · Answer 6 · 2023-10-25 03:53:31

121

Views

Prove that if $m^2$ is even then $m$ is even

Published on 25 Oct 2023 - 3:53

score 60 · Answer 7 · 2023-10-27 23:57:31

60

Views

Do exist positive integers $a < b$ with the following property: Whenever $m, n$ are positive integers with $m^a|n^b$ then $m|n$.

Published on 27 Oct 2023 - 23:57

score 288 · Answer 8 · 2023-10-29 18:21:56

288

Views

Solution Verification for RMO (Indian Math Competition)

Published on 29 Oct 2023 - 18:21

score 57 · Answer 9 · 2023-11-01 11:31:57

57

Views

For prime $p$, show that $p\mid a^n\Rightarrow p\mid a$

Published on 01 Nov 2023 - 11:31

score 93 · Answer 10 · 2023-11-01 15:03:06

93

Views

Find $n$ knowing some divisibilities

Published on 01 Nov 2023 - 15:03

score 50 · Answer 11 · 2023-11-03 00:04:19

50

Views

If primes $p_1 \neq p_2$ divide $n$, then $\exists$ $x, y \in G \setminus \{e\}$ such that $\langle{x}\rangle \cap \langle{y}\rangle = \{e\}$

Published on 03 Nov 2023 - 0:04

score 195 · Answer 12 · 2026-02-23 13:46:12

195

Views

What is the remainder when dividing $a$ by $5$ if $\sum_{k=1}^{1992}\frac{1}{k}=\frac{a}{b}$?

Published on 23 Feb 2026 - 13:46

score 194 · Answer 13 · 2023-11-07 19:01:44

194

Views

Formally prove that $3^ {80} - 2^{20}$ divisible by $5$

Published on 07 Nov 2023 - 19:01

score 71 · Answer 14 · 2026-03-29 18:51:02

71

Views

Find all positive integers m so that for $n=4m (2^m - 1)$, $n | (a^m - 1)$ for all a coprime to n

Published on 29 Mar 2026 - 18:51

score 44 · Answer 15 · 2023-11-09 05:41:28

44

Views

Another Binomial Coefficient Congruence Modulo Prime Powers

Published on 09 Nov 2023 - 5:41

List Question

Find N such that for all x $\ge$ N, $P(x)$ is Divisible by Primes Bigger than 10

Given $a,b \in \mathbb{N}$, is it true that $\phi(\gcd(a,b))=\gcd(\phi(a),\phi(b))$?

Prove that a*b is not divisible by prime number p

Formulas that generate "too few" primes

Why do all parasitic numbers seem to be multiples of repunits?

Prove that if $m^2$ is even then $m$ is even

Do exist positive integers $a < b$ with the following property: Whenever $m, n$ are positive integers with $m^a|n^b$ then $m|n$.

Solution Verification for RMO (Indian Math Competition)

For prime $p$, show that $p\mid a^n\Rightarrow p\mid a$

Find $n$ knowing some divisibilities

If primes $p_1 \neq p_2$ divide $n$, then $\exists$ $x, y \in G \setminus \{e\}$ such that $\langle{x}\rangle \cap \langle{y}\rangle = \{e\}$

What is the remainder when dividing $a$ by $5$ if $\sum_{k=1}^{1992}\frac{1}{k}=\frac{a}{b}$?

Formally prove that $3^ {80} - 2^{20}$ divisible by $5$

Find all positive integers m so that for $n=4m (2^m - 1)$, $n | (a^m - 1)$ for all a coprime to n

Another Binomial Coefficient Congruence Modulo Prime Powers

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