Question

When the expression $p^2 - pq + q^2$ is divisible by 3?

score 650 · Answer 1 · 2026-04-12 20:24:35

650

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When the expression $p^2 - pq + q^2$ is divisible by 3?

Published on 12 Apr 2026 - 20:24

score 191 · Answer 2 · 2026-04-03 17:52:43

191

Views

Elementary proof of $\gcd(a, b) = 1 \wedge a\ |\ b\ c \Rightarrow a \ | \ c $

Published on 03 Apr 2026 - 17:52

score 141 · Answer 3 · 2026-04-13 20:02:49

141

Views

Any composite natural number divides the product of two smaller natural numbers

Published on 13 Apr 2026 - 20:02

score 102 · Answer 4 · 2015-11-20 21:12:44

102

Views

proving for all odd integers that $n^2 + 2n \equiv 0 \pmod{3}$

Published on 20 Nov 2015 - 21:12

score 152 · Answer 5 · 2015-11-21 00:09:01

152

Views

Prove that the product of the two middle divisors of a number $N$ is equal to $N$

Published on 21 Nov 2015 - 0:09

score 976 · Answer 6 · 2026-04-12 02:35:06

976

Views

How to prove that a polynomial at integer arguments is always divisible by $11520$?

Published on 12 Apr 2026 - 2:35

score 817 · Answer 7 · 2015-11-22 17:25:27

817

Views

How many integers between $10000$ and $99999$, inclusive, are divisible by $3$ or $5$ or $7?$

Published on 22 Nov 2015 - 17:25

score 28 · Answer 8 · 2015-11-22 18:59:26

28

Views

Prove divisibility: If $j_1\mid j_2$ and $j_2\mid j_1$, then $j_1 = \pm j_2$

Published on 22 Nov 2015 - 18:59

score 98 · Answer 9 · 2015-11-23 01:18:12

98

Views

Proving that $a+b+c $ is composite knowing it divides $abc$

Published on 23 Nov 2015 - 1:18

score 355 · Answer 10 · 2026-03-30 12:23:40

355

Views

Number theory primes and congruences: $p^{32} -1$ is divisible by $16320$

Published on 30 Mar 2026 - 12:23

score 77 · Answer 11 · 2026-04-13 01:09:27

77

Views

Find ( a + b + c) if $4a1b4c9$ is divisible by $99$

Published on 13 Apr 2026 - 1:09

score 67 · Answer 12 · 2026-04-01 00:24:29

67

Views

Geometrization of the positive integers

Published on 01 Apr 2026 - 0:24

score 297 · Answer 13 · 2015-11-24 14:55:22

297

Views

What does mean this notation $q \mid k$?

Published on 24 Nov 2015 - 14:55

score 458 · Answer 14 · 2015-11-25 12:55:22

458

Views

Proof by contradiction : if n or m are not divisible by 3 then the sum or the difference is also not divisible by 3

Published on 25 Nov 2015 - 12:55

score 630 · Answer 15 · 2026-04-11 21:59:25

630

Views

Proving ${\rm gcd}(a,b)=1$, $a\mid c$ and $b\mid c$ implies $ab\mid c$ WITHOUT Euclid's or Bezout's lemma.

Published on 11 Apr 2026 - 21:59

List Question

When the expression $p^2 - pq + q^2$ is divisible by 3?

Elementary proof of $\gcd(a, b) = 1 \wedge a\ |\ b\ c \Rightarrow a \ | \ c $

Any composite natural number divides the product of two smaller natural numbers

proving for all odd integers that $n^2 + 2n \equiv 0 \pmod{3}$

Prove that the product of the two middle divisors of a number $N$ is equal to $N$

How to prove that a polynomial at integer arguments is always divisible by $11520$?

How many integers between $10000$ and $99999$, inclusive, are divisible by $3$ or $5$ or $7?$

Prove divisibility: If $j_1\mid j_2$ and $j_2\mid j_1$, then $j_1 = \pm j_2$

Proving that $a+b+c $ is composite knowing it divides $abc$

Number theory primes and congruences: $p^{32} -1$ is divisible by $16320$

Find ( a + b + c) if $4a1b4c9$ is divisible by $99$

Geometrization of the positive integers

What does mean this notation $q \mid k$?

Proof by contradiction : if n or m are not divisible by 3 then the sum or the difference is also not divisible by 3

Proving ${\rm gcd}(a,b)=1$, $a\mid c$ and $b\mid c$ implies $ab\mid c$ WITHOUT Euclid's or Bezout's lemma.

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