List questions from divisibility

Published on 12 Apr 2026 - 1:34

402

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Proof for divisibilty tests for 13, 16, 17,19

Published on 14 Apr 2026 - 8:52

5.2k

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Proof that lcm(a,b) = ab/gcd(a,b)

Published on 11 Apr 2026 - 23:48

113

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Show that if $a\mid b$ then $2^a-1\mid 2^b-1$

Published on 15 Apr 2026 - 16:59

101

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Let $m$ and integer and $d$ divisor of $m$. How to prove that $\gcd$ of certain numbers is $m/d$?

Published on 16 Apr 2026 - 9:23

563

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Show that if $ \gcd(a,b)=d,\gcd(a,c)=f,\gcd(b,c)=1 \ \Rightarrow\gcd(a,bc)=df$

Published on 16 Apr 2026 - 9:33

39

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Show that if $d_1e_1=d_2e_2,\ and\ \gcd(e_1,e_2)=1\Rightarrow\ lcm(d_1,d_2)=d_1e_1=d_2e_2$

Published on 17 Apr 2026 - 11:06

351

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How do I show that $2730$ divides $n^{13}-n$ for $n$ is integer?

Published on 14 Apr 2026 - 13:08

1k

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Prove by strong induction that $3^n$ divides $a_n$ for all integers $n \ge 1$

Published on 16 Apr 2026 - 13:06

96

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Proof checking Number theory: prove that $d\nmid a^{2^{n}}+1$.

Published on 29 Mar 2026 - 16:31

370

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Prove that a perfect square (also a perfect square backwards) is divisible by 121

Published on 25 Mar 2026 - 22:25

42

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Help - remainders when number is divided

Published on 12 Apr 2026 - 3:43

1k

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Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$

Published on 15 Apr 2026 - 7:06

54

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Properties involving prime factorization and divisibility

Published on 10 Apr 2026 - 23:56

624

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Divisibility via Induction: $8^n\mid (4n)!$

Published on 12 Apr 2026 - 20:47

List Question

Two numbers from any 51 integers must differ by 50?? (Textbook error?)

Proof for divisibilty tests for 13, 16, 17,19

Proof that lcm(a,b) = ab/gcd(a,b)

Show that if $a\mid b$ then $2^a-1\mid 2^b-1$

Let $m$ and integer and $d$ divisor of $m$. How to prove that $\gcd$ of certain numbers is $m/d$?

Show that if $ \gcd(a,b)=d,\gcd(a,c)=f,\gcd(b,c)=1 \ \Rightarrow\gcd(a,bc)=df$

Show that if $d_1e_1=d_2e_2,\ and\ \gcd(e_1,e_2)=1\Rightarrow\ lcm(d_1,d_2)=d_1e_1=d_2e_2$

How do I show that $2730$ divides $n^{13}-n$ for $n$ is integer?

Prove by strong induction that $3^n$ divides $a_n$ for all integers $n \ge 1$

Proof checking Number theory: prove that $d\nmid a^{2^{n}}+1$.

Prove that a perfect square (also a perfect square backwards) is divisible by 121

Help - remainders when number is divided

Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$

Properties involving prime factorization and divisibility

Divisibility via Induction: $8^n\mid (4n)!$

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