Vaishali

3 Questions
0 Answers

0

257

0

+12

function

a function f is defined on the positive integers. it is given that f is non-decreasing, that f(2) = 2, and that f(mn) = f(m)f(n) for m and n relatively prime. prove that f(4) f(13) >= [f(7)]^2

Vaishali Aug 12, 2021

0

401

1

+12

prove that (3+2√2)^2n-1 + (3-2√2)^2n-1 - 2 is a perfect integral square

prove that (3+2√2)^2n-1 + (3-2√2)^2n-1 - 2 is a perfect integral square for every positive integer n.

Vaishali Aug 12, 2021

0

300

1

+12

sum of three positive real numbers by the sum of their reciprocals is always atleast 9

Show that the product of the sum of three positive real numbers by the sum of their reciprocals is always atleast 9. When can the product be exactly 9?

Vaishali Aug 12, 2021