(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(n) is function that takes input n and outputs the smallest integer grater that n^pi

prove that there exists natural numbers abcdwxyz that are all not smaller than 2015 such that equation is satisfied

f(x) + f(y) + f(z) + f(w) = f(a) + f(b) + f(c) + f(d)

and they abcd and wxyz are not trivial meaning that a,b,c,d is not equal to w,x,y,z

2. Relevant equations

well ordering principal

or maybe induction

3. The attempt at a solution

f(x) + f(y) + f(z) + f(w) = f(a) + f(b) + f(c) + f(d)

f(x) = [x^pi + 1]

f(y) = [y^pi + 1]

and so on

[x] means greatest number smaller than x for example [32.23] = 32 [12.99] = 12

let x_{0}be the smallest x that satisfies the equation

and i am stuck i don't know what to do afterwards

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# Homework Help: Prove that the equation is satisfied at least once

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