# Searching for a conjecture that is true until the 127 power of n. [duplicate]

This question already has an answer here:

I am searching for a mathematical conjecture that is true until something like n = 117, or n = 127, or a number close.

It is an equality, a formula implying calcultations to the power of n, IIRC.

What is the name of this conjecture ?

Why do I search for this formula ?:

I had read an article a few years ago that was discussing about experiments around the validation of a theory in Science, namely in Physics.

The example of this conjecture was given so as to convince that you can choose to repeat an experiment with different parameters a certain number of time, ultimately in the end, it does not give the entire certainty a physical theory is true: it just happens we still haven't found any outlier measurement that contracdicts the physical theory.

As a matter of fact, we can test this mathematical conjecture for the first 127 integers, which is a bunch of times, and believe it is always true, whereas it is false for all n.

I would like the name of it so as to be able to name it / source it in discussion.

Does it ring any bell for you ?

## marked as duplicate by Ethan Bolker, YuiTo Cheng, Community♦Jul 11 at 10:25

• – twnly Jul 11 at 9:45
• Like the conjecture that can easily be proved by induction that $\;n\le116\;$ ? Or also that $\;n^2-117n<0\;$ ?... – DonAntonio Jul 11 at 9:45
• – Ethan Bolker Jul 11 at 9:50
• You can modify the Borwein integral to get something to this effect. – Tony S.F. Jul 11 at 10:01
• Although I have not recognized at first look the conjecture I had in mind, all of the resources you pointed me to are answering my need. Now I need to choose the most explicit example. I tend to think I will choose this one: math.stackexchange.com/a/365881/6235 . n17+9 and (n+1)17+9 are relatively prime The first counterexample is n=8424432925592889329288197322308900672459420460792433 – Stephane Rolland Jul 11 at 10:28

• Not at all the conjecture I was searching for: But it is sort of a really good example nonetheless!!! Imagine an algorithm using binary representation of integers on one byte as you said, and the law/function/operation f(x)=x+1. Without testing more than 127 values, one cannot guess the the Law is cyclical, or that it has a singularity like 1/0 higher, or could even be topped/constant for any number > 127. In any case, the validity of the intuition that the Law always gives the upper integer is wrong, the intuition only cannot justify to make it a rule for all n. Great simple example – Stephane Rolland Jul 11 at 11:06