Question

Solve the system:$\,\small\begin{eqnarray}a_1P+b_1Q+c_1R&=&0\\ a_2P+b_2Q+c_2R&=&0\\ a_3P+b_3Q+c_3R&=&0 \end{eqnarray}$ where $\small PQR\neq 0$

score 96 · Answer 1 · 2015-11-30 16:24:31

Solve the system:$\,\small\begin{eqnarray}a_1P+b_1Q+c_1R&=&0\\ a_2P+b_2Q+c_2R&=&0\\ a_3P+b_3Q+c_3R&=&0 \end{eqnarray}$ where $\small PQR\neq 0$

score 1.4k · Answer 2 · 2026-04-01 03:44:16

1.4k

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Published on 01 Apr 2026 - 3:44

score 117 · Answer 3 · 2015-12-01 01:59:07

117

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Find all values of $n$ for which the Diophantine equation $n=a^2-b^2$ has a solution

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score 475 · Answer 4 · 2015-12-01 16:05:07

475

Views

integer solution of $\frac{x^3+y^3+z^3-xy(x+y)-yz(y+z)-xz(x+z)-2xyz}{(x+y+z)(x+y-z)(x-y+z)(x-y-z)}=\frac{1}{2016}$

Published on 01 Dec 2015 - 16:05

score 115 · Answer 5 · 2026-03-28 17:41:21

115

Views

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Published on 28 Mar 2026 - 17:41

score 132 · Answer 6 · 2015-12-03 19:00:44

132

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score 47 · Answer 7 · 2015-12-03 22:33:06

47

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score 122 · Answer 8 · 2015-12-04 15:55:15

122

Views

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score 129 · Answer 9 · 2026-04-10 12:03:56

129

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score 137 · Answer 10 · 2015-12-04 18:07:03

137

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score 166 · Answer 11 · 2015-12-04 19:10:53

166

Views

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score 33 · Answer 12 · 2026-04-01 07:20:42

33

Views

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score 33 · Answer 13 · 2015-12-05 05:57:36

33

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score 56 · Answer 14 · 2026-03-28 01:14:32

56

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score 48 · Answer 15 · 2015-12-05 17:36:23

48

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Is the diophantine equation $a = x^p - y^p$ sufficient to find $x$ and $y$ in terms of $a$ and $p$?

Published on 05 Dec 2015 - 17:36

List Question

Solve the system:$\,\small\begin{eqnarray}a_1P+b_1Q+c_1R&=&0\\ a_2P+b_2Q+c_2R&=&0\\ a_3P+b_3Q+c_3R&=&0 \end{eqnarray}$ where $\small PQR\neq 0$

Find all positive integers $n$ such that $2^8+2^{12}+2^n$ is a perfect square

Find all values of $n$ for which the Diophantine equation $n=a^2-b^2$ has a solution

integer solution of $\frac{x^3+y^3+z^3-xy(x+y)-yz(y+z)-xz(x+z)-2xyz}{(x+y+z)(x+y-z)(x-y+z)(x-y-z)}=\frac{1}{2016}$

$Dm^2 - n^2D^2$ is a perfect square then $D$ is the sum of two squares

solution of Diofantine equation

Show that if a Diophantine equation has a solution then both $x$ and $y$ must be odd

$f (x) \in\mathbb Z[x]$ be such that $f$ is a perfect $k$-th power on taking positive integer values . Is $f$ a perfect $k$-th power?

Proving a power Diophantine equation has no solutions

Prove for $abc$-triples that $c\leq rad(abc)^2$

Show that a cubic Diophantine equation has no solutions

What determines the number of families to $1-4x-4(1-x^2)z = w^2$?

Prove 3 diophantine expressions cannot simultaneously be perfect squares

Impossible form of a triangular number

Is the diophantine equation $a = x^p - y^p$ sufficient to find $x$ and $y$ in terms of $a$ and $p$?

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