Prove that a^2|b and b^3|c then a^4b^5|c^3.  TOPIC_SOLVED

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Prove that a^2|b and b^3|c then a^4b^5|c^3.

Postby ggfied on Sun Apr 14, 2013 3:04 am

Hi i'm new to this forum. I have a problem with a question on number theory which requires proving. The question is "Let a, b, c be integers. Prove that if a^2|b and b^3|c then a^4b^5|c^3." I do not know how to go around to solve this question please help thanks.

I tried expanding a^2|b and b^3|c to a^2=bk where some k is an integer and b^3=cl where some l is an integer multiplying it together a^2b^3=bckl cube both sides a^6b^8=c^3kl
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Re: Prove that a^2|b and b^3|c then a^4b^5|c^3.  TOPIC_SOLVED

Postby rsood on Wed Aug 07, 2013 12:14 am

a^2|b so b = a * a * j
b^3|c so c = b * b * b * k
c^3 = b * b * b * k * b * b * b * k * b * b * b * k = b * b * b * k * b * b * b * k * b * a * a * j * a * a * j * k = a^4 * b^7 * j^2 * k^3
a^4 * b^7 * j^2 * k^3/a^4b^5 = b^2 * j^2 * k^3, which is an integer, so a^4b^5 | c^3
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