MathDB

p1. Show that

9x + 5y

is a multiple of

17

whenever

2x + 3y

is a multiple of

17

.
p2. Express the five distinct fifth roots of

1

in terms of radicals.
p3. Prove that the three perpendiculars dropped to the three sides of an equilateral triangle from any point inside the triangle have a constant sum.
p4. Find the volume of a sphere which circumscribes a regular tetrahedron of edge

a

.
p5. For any integer

n

greater than

1

, show that

n^2-2n + 1

is a factor at

n^{n-1}-1

.
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here.

Problem Statement