Question on theorem of arithmetic euclid's algorithm

singedang2
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i know this question has to do with theorem of arithmetic and euclidean algorithm, but i don't even know where to start. help pls! thank you!
 
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How about an argument using induction?
 
i don't think this can proven with induction... any other comments?
 
Try comparing prime factorizations of a and b. Suppose a prime p appears as p^k in the prime factorization of a and as p^m in the prime factorization of b.

what do those divisbility critrea tell you about m and k?
 
tell me more about this... gahhh i don't quite get it.
 
Start with the first condition, a|b^2. You should be able to come up with an inequality for k and m from this.

How does divisibility relate to the exponents in a prime factorization?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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