# Assignment 10, STEP question ib

Happy New Year STEPpers !

Looking at the aforementioned bit of the STEP question in this assignment, I notice that candidates are invited to show that f(N) is an integer 'for all N' , where f(N) has only been defined for N in Z-plus.

This surely leads to an 'embarrassing bit' at the end, where all one can do is say that until a form of f(N) , true for all N, is presented (or found, presumably by us), it is not possible to extend a result for f(N) : N in Z-plus to a result for all N.

I concede that this is a STEP II question but are we meant to find a form of f(N) which holds for C and so on? Or can we breathe a sigh of relief and let 'all N' be 'all N as defined at the top of the question' , i.e all N in Z-plus?

Thanks,

Bogan

### N

Happy New Year!

Since the "Stem" of the question states that $N$ is a positive integer, then this holds for the whole question. So when asked to show that $f(N)$ is an integer for all $N$ this means for all positive integers.

(Note - if $N$ being a positive integer was declared in part (i), or part (ii) then you could only assume that it applies to that part).

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP