Graph Theory
by JetFire008, Mar 21, 2025, 4:22 PM
Prove that for any Hamiltonian cycle, if it contain edge
, then it must not contain edge
.


Inspired by hunghd8
by sqing, Mar 21, 2025, 4:08 PM
Inspired by hunghd8
by sqing, Mar 21, 2025, 3:36 PM
Let
and
Prove that










This post has been edited 1 time. Last edited by sqing, 2 hours ago
Prime for square numbers
by giangtruong13, Mar 21, 2025, 2:43 PM
Given that
are natural numbers satisfy that:
and
are prime numbers. Prove that
is a perfect squared number




This post has been edited 1 time. Last edited by giangtruong13, 3 hours ago
Assisted perpendicular chasing
by sarjinius, Mar 9, 2025, 3:41 PM
In acute triangle
with circumcenter
and orthocenter
, let
be an arbitrary point on the circumcircle of triangle
such that
does not lie on line
and that line
is not parallel to line
. Let
be the point on the circumcircle of triangle
such that
is perpendicular to
, and let
be the point on line
such that
. Let
and
be the points on the circumcircle of triangle
such that
is a diameter, and
and
are parallel. Let
be the midpoint of
.
(a) Show that
and
are perpendicular.
(b) Show that
and
are perpendicular.
























(a) Show that


(b) Show that


Interesting inequality
by sqing, Feb 26, 2025, 9:30 AM
a! + b! = 2^{c!}
by parmenides51, Mar 26, 2024, 3:44 PM
Determine all triples
of positive integers such that

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(Walther Janous)
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