Question

Largest integer $n$ such that $3^n$ divides every $abc$ with $a$, $b$, $c$ positive integers, $a^2+b^2=c^2$, and $3|c$

score 233 · Answer 1 · 2018-04-22 06:44:49

Largest integer $n$ such that $3^n$ divides every $abc$ with $a$, $b$, $c$ positive integers, $a^2+b^2=c^2$, and $3|c$

Published on 22 Apr 2018 - 6:44

score 45 · Answer 2 · 2018-04-22 08:46:58

Is it true always that if for every $a,b,c\in \mathbb{N}$ and $a^2+b^2=c^2$, such that if $3|c$, then $abc$ is a multiple of $3^4$

score 40 · Answer 3 · 2026-03-21 19:23:12

40

Views

Divisibility conditions

Published on 21 Mar 2026 - 19:23

score 85 · Answer 4 · 2026-03-25 12:53:15

85

Views

If $a\mid b$ and $a>0$ then $(a,b)=a$

Published on 25 Mar 2026 - 12:53

score 60 · Answer 5 · 2018-04-25 10:50:09

60

Views

Fundamental assumption about number theory: divisibility

Published on 25 Apr 2018 - 10:50

score 1.5k · Answer 6 · 2026-03-25 07:42:50

1.5k

Views

Smallest number with at least $n$ divisors.

Published on 25 Mar 2026 - 7:42

score 18.6k · Answer 7 · 2018-04-26 17:47:24

18.6k

Views

Prove that $7^n - 1$ is divisible by 6

Published on 26 Apr 2018 - 17:47

score 77 · Answer 8 · 2018-04-26 20:45:55

77

Views

Divisibility of $n^2+9$ by $n+3$

Published on 26 Apr 2018 - 20:45

score 28 · Answer 9 · 2018-04-27 15:10:42

28

Views

Determine the divisor so that the quotient is less than 6,000.

Published on 27 Apr 2018 - 15:10

score 886 · Answer 10 · 2018-04-28 14:23:56

886

Views

Let $n=(6t+1)(12t+1)(18t+1)$. Show that $a^{n-1} \equiv 1\pmod n$ if $(a,n)=1$

Published on 28 Apr 2018 - 14:23

score 149 · Answer 11 · 2026-03-25 07:41:58

149

Views

Prove that $100|11^{10} - 1$

Published on 25 Mar 2026 - 7:41

score 61 · Answer 12 · 2018-04-30 08:09:42

61

Views

Where can I read the rules on the algabraic manipulation needed to finish this inductive proof that $133$ divides $11^{k+1}+12^{2k-1}$?

Published on 30 Apr 2018 - 8:09

score 1.3k · Answer 13 · 2018-04-30 17:41:30

1.3k

Views

Can $n - 1$ divide $n$, where $n$ is a positive, composite integer?

Published on 30 Apr 2018 - 17:41

score 143 · Answer 14 · 2018-05-02 08:56:01

143

Views

Find all positive integer $a,b$, such that $[a,b+2017]=[a+2017,b]$.

Published on 02 May 2018 - 8:56

score 40 · Answer 15 · 2018-05-02 15:08:10

40

Views

Modular Arithmetic Problem (Dividing by 3)

Published on 02 May 2018 - 15:08

List Question

Largest integer $n$ such that $3^n$ divides every $abc$ with $a$, $b$, $c$ positive integers, $a^2+b^2=c^2$, and $3|c$

Is it true always that if for every $a,b,c\in \mathbb{N}$ and $a^2+b^2=c^2$, such that if $3|c$, then $abc$ is a multiple of $3^4$

Divisibility conditions

If $a\mid b$ and $a>0$ then $(a,b)=a$

Fundamental assumption about number theory: divisibility

Smallest number with at least $n$ divisors.

Prove that $7^n - 1$ is divisible by 6

Divisibility of $n^2+9$ by $n+3$

Determine the divisor so that the quotient is less than 6,000.

Let $n=(6t+1)(12t+1)(18t+1)$. Show that $a^{n-1} \equiv 1\pmod n$ if $(a,n)=1$

Prove that $100|11^{10} - 1$

Where can I read the rules on the algabraic manipulation needed to finish this inductive proof that $133$ divides $11^{k+1}+12^{2k-1}$?

Can $n - 1$ divide $n$, where $n$ is a positive, composite integer?

Find all positive integer $a,b$, such that $[a,b+2017]=[a+2017,b]$.

Modular Arithmetic Problem (Dividing by 3)

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