Question

How does one show that for $k \in \mathbb{Z_+},3\mid2^{2^k} +5$ and $7\mid2^{2^k} + 3, \forall \space k$ odd.

score 85 · Answer 1 · 2015-02-19 18:35:34

85

Views

How does one show that for $k \in \mathbb{Z_+},3\mid2^{2^k} +5$ and $7\mid2^{2^k} + 3, \forall \space k$ odd.

Published on 19 Feb 2015 - 18:35

score 219 · Answer 2 · 2015-02-20 06:39:02

219

Views

GCD of many numbers

Published on 20 Feb 2015 - 6:39

score 99 · Answer 3 · 2015-02-20 21:13:00

99

Views

Arithmetic mean 6 times greater than GCD?

Published on 20 Feb 2015 - 21:13

score 188 · Answer 4 · 2015-02-20 21:49:28

188

Views

Prove that if $a, b$ are any positive integers $>1$, then either $a$ or $b$ or $a+b$ or $a-b$ is divisible by 3.

Published on 20 Feb 2015 - 21:49

score 205 · Answer 5 · 2026-04-09 04:20:44

205

Views

Efficiently producing certain kinds of examples of the application of Euclid's algorithm

Published on 09 Apr 2026 - 4:20

score 63 · Answer 6 · 2026-04-08 16:26:19

63

Views

Put this word problem into math terms: A man goes to a stream....

Published on 08 Apr 2026 - 16:26

score 96 · Answer 7 · 2026-04-02 18:39:18

96

Views

Divisibility problem using Wilson's theorem: $4(p-3)! + 2$ is divisible by $p$

Published on 02 Apr 2026 - 18:39

score 1.1k · Answer 8 · 2026-02-23 21:34:17

1.1k

Views

What does a distributed lattice have to do with GCD and LCM?

Published on 23 Feb 2026 - 21:34

score 1.5k · Answer 9 · 2026-04-09 05:37:55

1.5k

Views

Finding missing digits in factorials

Published on 09 Apr 2026 - 5:37

score 215 · Answer 10 · 2015-02-24 20:30:06

215

Views

$\operatorname{lcm}(a,b) = c$ and $\gcd(a,b) = d$ => $\operatorname{lcm}(\frac{a}{d},\frac{b}{d}) = \frac{c}{d}$ in a Euclidean domain or PID

Published on 24 Feb 2015 - 20:30

score 947 · Answer 11 · 2015-02-25 17:00:25

947

Views

Division rules for other number systems?

Published on 25 Feb 2015 - 17:00

score 68 · Answer 12 · 2015-02-25 17:10:35

68

Views

Show $\nexists k:3^7\mid k!$ but $3^8\nmid k!$

Published on 25 Feb 2015 - 17:10

score 2.9k · Answer 13 · 2015-02-25 18:04:36

2.9k

Views

How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?

Published on 25 Feb 2015 - 18:04

score 117 · Answer 14 · 2015-02-25 20:30:11

117

Views

How can I demonstrate that $x-x^9$ is divisible by 30?

Published on 25 Feb 2015 - 20:30

score 157 · Answer 15 · 2026-03-31 17:18:23

157

Views

proof : $a,b \in N, a^5 | b^5 \rightarrow a | b$

Published on 31 Mar 2026 - 17:18

List Question

How does one show that for $k \in \mathbb{Z_+},3\mid2^{2^k} +5$ and $7\mid2^{2^k} + 3, \forall \space k$ odd.

GCD of many numbers

Arithmetic mean 6 times greater than GCD?

Prove that if $a, b$ are any positive integers $>1$, then either $a$ or $b$ or $a+b$ or $a-b$ is divisible by 3.

Efficiently producing certain kinds of examples of the application of Euclid's algorithm

Put this word problem into math terms: A man goes to a stream....

Divisibility problem using Wilson's theorem: $4(p-3)! + 2$ is divisible by $p$

What does a distributed lattice have to do with GCD and LCM?

Finding missing digits in factorials

$\operatorname{lcm}(a,b) = c$ and $\gcd(a,b) = d$ => $\operatorname{lcm}(\frac{a}{d},\frac{b}{d}) = \frac{c}{d}$ in a Euclidean domain or PID

Division rules for other number systems?

Show $\nexists k:3^7\mid k!$ but $3^8\nmid k!$

How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?

How can I demonstrate that $x-x^9$ is divisible by 30?

proof : $a,b \in N, a^5 | b^5 \rightarrow a | b$

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