SOLUTION: Let a and b be positive integers, assume that (a^(3))|(b^(3)). How do i prove tha a|b using prime factorization of a and b.

Question 26480: Let a and b be positive integers, assume that (a^(3))|(b^(3)).
How do i prove tha a|b using prime factorization of a and b.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Let a and b be positive integers, assume that (a^(3))|(b^(3)).
How do i prove tha a|b using prime factorization of a and b.
LET A ={(A1)^P1}{(A2)^P2}{(A3)^P3}....ETC...WHERE,A1,A2,A3 ARE ALL PRIME INTEGERS AND P1,P2,P3,ETC ARE INTEHERS.SIMILARLY.....
LET B ={(B1)^Q1}{(B2)^Q2}{(B3)^Q3}....ETC...WHERE,B1,B2,B3 ARE ALL PRIME INTEGERS AND Q1,Q2,Q3,ETC ARE INTEHERS
HENCE A^3={(A1)^3P1}{(A2)^3P2}{(A3)^3P3}....ETC..AND
B ={(B1)^3Q1}{(B2)^3Q2}{(B3)^3Q3}....ETC.......
NOW IF A^3|B^3.....ALL OF THE PRIME FACTORS OF A^3 SHALL BE CONTAINED IN B^3..
THUS {(A1)^3P1}{(A2)^3P2}{(A3)^3P3}....ETC..ARE CONTAINED IN B^3.
HENCE OBVIOUSLY ALL PRIME FACTORS OF A...NAMELY...{(A1)^P1}{(A2)^P2}{(A3)^P3}....ETC..ARE CONTAINED IN B...HENCE A|B
RELATED QUESTIONS
Let a not equal 0, b and c be integers with a and b relatively prime. Show that if a|b*c (answered by venugopalramana)

Let and be relatively prime integers with a > b > 0 and (a^3 - b^3)/(a-b)^3= 73/3. What... (answered by greenestamps)

Could you please help me prove the following mathematical statement. Let p be a prime... (answered by richard1234)

Let a,b,c,and d be positive. Prove the follwing properties of the proportion a/b=c/d. (answered by jim_thompson5910)

I do not even know where to start with this proof. Prove or disprove: let a, b, and c... (answered by ikleyn)

Let a,b,c be integers such that a^2+b^2 = c^2. For c divisible by 3, prove that a and b... (answered by ikleyn)

To show that is an irrational number unless n is a perfect square, explain how the... (answered by solver91311)

Let G be a group and let a b be some elements of G. Prove or disprove the following... (answered by jorel1380)

let. a, b, c, d be positive integers and (log( b)/log (a))=3/2 ,(log (d)/log (c))=5/4 (answered by Edwin McCravy)