Question

Prove that, $(2\cdot 4 \cdot 6 \cdot ... \cdot 4000)-(1\cdot 3 \cdot 5 \cdot ...\cdot 3999)$ is a multiple of $2001$

score 5.1k · Answer 1 · 2026-03-26 17:42:30

5.1k

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Prove that, $(2\cdot 4 \cdot 6 \cdot ... \cdot 4000)-(1\cdot 3 \cdot 5 \cdot ...\cdot 3999)$ is a multiple of $2001$

Published on 26 Mar 2026 - 17:42

score 97 · Answer 2 · 2014-12-09 19:44:57

97

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Alternate way to Prove or disprove $6\mid n(n+1)(n+2)$

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score 1.5k · Answer 3 · 2014-12-09 21:19:02

1.5k

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Is there a quick parity test for integers expressed with odd radicies?

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score 3.5k · Answer 4 · 2026-03-27 13:27:36

3.5k

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Show natural numbers ordered by divisibility is a distributive lattice.

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score 1.3k · Answer 5 · 2026-03-26 11:07:08

1.3k

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Prove that if $2|(x^2-1)$, then $8|(x^2-1)$.

Published on 26 Mar 2026 - 11:07

score 80 · Answer 6 · 2014-12-10 05:52:05

80

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Divisibility of numbers between $n^3$ and $n^3+n$

Published on 10 Dec 2014 - 5:52

score 137 · Answer 7 · 2014-12-10 10:59:41

137

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What does the "or" symbol mean as in "$ d\mid a$"

Published on 10 Dec 2014 - 10:59

score 92 · Answer 8 · 2026-03-30 12:57:06

92

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Prove the relation on $\Bbb N \setminus \{0,1\}$ is a partial order

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score 3.2k · Answer 9 · 2014-12-10 21:46:21

3.2k

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Prove by induction that an expression is divisible by 11

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score 233 · Answer 10 · 2026-03-26 17:34:37

233

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Trying to prove a congruence for Stirling numbers of the second kind

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score 36 · Answer 11 · 2014-12-11 03:53:13

36

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Proving divisibility of b and a

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score 47 · Answer 12 · 2014-12-11 06:39:07

47

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Which number is divisible by $3^6$?

Published on 11 Dec 2014 - 6:39

score 235 · Answer 13 · 2014-12-11 08:46:46

235

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Find the greatest common divisor of $8^{10}+12$ and $8^5$ without a calculator.

Published on 11 Dec 2014 - 8:46

score 307 · Answer 14 · 2014-12-11 16:13:00

307

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Show that the number $n$ is divisible by $7$

Published on 11 Dec 2014 - 16:13

score 57 · Answer 15 · 2014-12-11 19:07:34

57

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Can this simple divisibility property on binomial coefficient be proved without Gauss' lemma?

Published on 11 Dec 2014 - 19:07

List Question

Prove that, $(2\cdot 4 \cdot 6 \cdot ... \cdot 4000)-(1\cdot 3 \cdot 5 \cdot ...\cdot 3999)$ is a multiple of $2001$

Alternate way to Prove or disprove $6\mid n(n+1)(n+2)$

Is there a quick parity test for integers expressed with odd radicies?

Show natural numbers ordered by divisibility is a distributive lattice.

Prove that if $2|(x^2-1)$, then $8|(x^2-1)$.

Divisibility of numbers between $n^3$ and $n^3+n$

What does the "or" symbol mean as in "$ d\mid a$"

Prove the relation on $\Bbb N \setminus \{0,1\}$ is a partial order

Prove by induction that an expression is divisible by 11

Trying to prove a congruence for Stirling numbers of the second kind

Proving divisibility of b and a

Which number is divisible by $3^6$?

Find the greatest common divisor of $8^{10}+12$ and $8^5$ without a calculator.

Show that the number $n$ is divisible by $7$

Can this simple divisibility property on binomial coefficient be proved without Gauss' lemma?

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