Derive from the theorem in question 61013 that
The numbers
In the Republic of mathematicians, the number
Author: A.V. Shapovalov
We call a triangle rational if all of its angles are measured by a rational number of degrees. We call a point inside the triangle rational if, when we join it by segments with vertices, we get three rational triangles. Prove that within any acute-angled rational triangle there are at least three distinct rational points.
Is there a positive integer
The number
Prove that in both of these sums, both terms are rational.
Author: A.K. Tolpygo
An irrational number
a) Prove that for some
b) Can it be that
Let
Prove that all