?
in natural numbers m and n.
is an integer. Prove that 
are integers.
satisfying 
Prove that 
Proposed by Phan Ngoc Chau
.
of moving 
unit in the positive direction and probability 
of moving 
.
,
;
.
be the sum of the products of the first 2000 positive integers, taken n at a time. For example, 
=
= the sum of the products of the 2000 positive integers, taken two at a time, etc. What is the value of 
+
+
?
be positive integers such that 
.
of 
(mod 
)
Y by
Prove that for each 
points in the plane, no three collinear and having integral distances from each other. If we have an infinite set of points with integral distances from each other, then all points are collinear.
(Anonymous314)
PS. wording needs to be fixed , source
points in the plane, no three collinear and having integral distances from each other. If we have an infinite set of points with integral distances from each other, then all points are collinear.(Anonymous314)
PS. wording needs to be fixed , source
This post has been edited 5 times. Last edited by parmenides51, Dec 5, 2022, 3:31 PM
