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

show that every positive integer can be written as the product of a square and a square-free integer (an integer that is not divisible by any perfect squares other than one

3. The attempt at a solution

well i can see by example that this works: i.e 60=2^{2}*3*5

Basically we want to show that any integer n>0 can be written as

n=p_{1}^{a1}p_{2}^{a2}...p_{k}^{ak}

if a_{i}is even, then its a perfect square

if a_{i}is odd, then p_{i}^{ai-1}is a perfect square and p_{i}is square free.

I dont know where to go from here... or if what i have said is correct

any help is appreciated

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# Homework Help: Every integer can be written as a sum of a square and square free integer

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