MathDB

p1. Suppose that

a

b

, and

c

are positive integers such that not all of them are even,

a < b

a^2 + b^2 = c^2

, and

c - b = 289

. What is the smallest possible value for

c

?
p2. If

a, b > 1

and

a^2

11

in base

b

, what is the third digit from the right of

b^2

in base

a

?
p3. Find real numbers

a, b

such that

x^2 - x - 1

is a factor of

ax^{10} + bx^9 + 1

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

Problem Statement