Proving the Property: Relatively Prime Factors and Division

Thread starter abcd8989
Start date Oct 23, 2010
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Property

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In the discussion on proving the property of relatively prime factors, it is established that if pq=ab and p and b are relatively prime, then p must be a factor of a and b must be a factor of q. The reasoning is that since ab equals pq, p divides ab, and due to the relative primality of p and b, p must specifically divide a. The argument is reinforced by suggesting a breakdown into prime factors for clarity. The symmetric nature of the argument is also noted, confirming the reverse relationship holds true. This establishes a clear connection between the factors when dealing with relatively prime integers.

Oct 23, 2010

abcd8989

If pq=ab where p, b are relatively prime, p must be a factor of a and b must be a factor of q.

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Oct 24, 2010

shoplifter

well, since ab = pq, p divides ab. but (p, b) = 1 and so p must divide a [this is obvious, trust me. if you don't see it, break them up into prime factors and deal with them case by case]. the other direction is symmetric.

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