Math Is Fun Forum

Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Some math problems

1. Find all integers n for which

is an integer.

2. Find a polynomial f(x) of degree 5 such that both of these properties hold:

f(x)-1 is divisible by

.

f(x) is divisible by

.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Some math problems

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Some math problems

Hi Enshrouded_;

1. Does this help...?

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Some math problems

A fact about 1. is that the difference between the result for two successive integers, f(n) - f(n-1), is:

which converges to +/- 1 very fast, suggesting that integers with an absolute value above 5 do not need to be checked.

Last edited by Relentless (2016-04-11 22:19:37)

Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Re: Some math problems

I still don't get how to do 1.

Nevermind I got it. I was thinking too hard.