SEARCH HOME
Math CentralQuandaries & Queries

search

Question from Naseer, a student:

I read somewhere that prime number can be a factor of square only if it occurs atleat twice in its square please explian this with examples.

thank you for your time

Hello,

Very loosely (not a rigorous proof) if a number is a square, say n = ztimesz and a prime p divides it, what do you think about p dividing z?

If p didn't divide z but divides n this would imply 'part' of p divided one of the z's and the 'rest' of p divided the other. However p is pime and can't be broken into parts thus p divides both z's and p2 divides n.

If you're familiar with the canonical representation of an integer n as a product of primes then the truth of your statement is obvious.

Penny

(editor's note) This is often called the "Fundamental Theorem of Arithmetic".

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS