Question

Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]

score 987 · Answer 1 · 2026-04-02 17:43:48

987

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Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]

Published on 02 Apr 2026 - 17:43

score 629 · Answer 2 · 2015-03-21 20:09:23

629

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For all integers $n \ge 1$, prove 6 divides $n(n+1)(n+2)$ by PMI.

Published on 21 Mar 2015 - 20:09

score 43 · Answer 3 · 2015-03-22 10:54:47

43

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Simple number theory

Published on 22 Mar 2015 - 10:54

score 64 · Answer 4 · 2015-03-22 12:31:54

If $x,y$ are integers greater than $1$ and $n$ is a positive integer such that $2^n + 1=xy$ , $\exists 1< a<n$ such that $2^a|x-1$ or $2^a|y-1$?

score 119 · Answer 5 · 2026-04-10 02:21:43

119

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Division by zero after removing factor.

Published on 10 Apr 2026 - 2:21

score 1.1k · Answer 6 · 2026-04-11 03:52:12

1.1k

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Proving divisibility of $a^3 - a$ by $6$

Published on 11 Apr 2026 - 3:52

score 8.3k · Answer 7 · 2015-03-24 13:55:14

8.3k

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Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.

Published on 24 Mar 2015 - 13:55

score 52 · Answer 8 · 2015-03-24 17:18:18

52

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Show that if $\gcd(r,s_1) =\gcd(r,s_2) = 1$, then $\gcd(r,s_1s_2) = 1$

Published on 24 Mar 2015 - 17:18

score 75 · Answer 9 · 2026-04-10 23:21:33

75

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For what positive integers is this number-theoretic equation true?

Published on 10 Apr 2026 - 23:21

score 136 · Answer 10 · 2026-04-10 16:49:13

136

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On Descartes numbers

Published on 10 Apr 2026 - 16:49

score 1.3k · Answer 11 · 2026-04-11 02:41:08

1.3k

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Quotient and Remainder of Numbers

Published on 11 Apr 2026 - 2:41

score 151 · Answer 12 · 2015-03-25 19:10:19

151

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$(z-k)$ is composite then $(z-1)+(k-1)$ is also composite(A proof for composite number).

Published on 25 Mar 2015 - 19:10

score 2.5k · Answer 13 · 2026-04-09 14:59:29

2.5k

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Is it possible to split a division problem into parts, like in multiplication?

Published on 09 Apr 2026 - 14:59

score 98 · Answer 14 · 2015-03-26 17:18:46

98

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Prove that for $n \gt 6$, there is a number $1 \lt k \lt n/2$ that does not divide $n$

Published on 26 Mar 2015 - 17:18

score 103 · Answer 15 · 2026-03-26 16:57:25

103

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On odd perfects and spoofs

Published on 26 Mar 2026 - 16:57

List Question

Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]

For all integers $n \ge 1$, prove 6 divides $n(n+1)(n+2)$ by PMI.

Simple number theory

If $x,y$ are integers greater than $1$ and $n$ is a positive integer such that $2^n + 1=xy$ , $\exists 1< a<n$ such that $2^a|x-1$ or $2^a|y-1$?

Division by zero after removing factor.

Proving divisibility of $a^3 - a$ by $6$

Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.

Show that if $\gcd(r,s_1) =\gcd(r,s_2) = 1$, then $\gcd(r,s_1s_2) = 1$

For what positive integers is this number-theoretic equation true?

On Descartes numbers

Quotient and Remainder of Numbers

$(z-k)$ is composite then $(z-1)+(k-1)$ is also composite(A proof for composite number).

Is it possible to split a division problem into parts, like in multiplication?

Prove that for $n \gt 6$, there is a number $1 \lt k \lt n/2$ that does not divide $n$

On odd perfects and spoofs

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