Let a and b be positive integers such that a^8 divides b^5. Show that a divides b.

Mathematics
Tutor: None Selected Time limit: 1 Day

Topic: Elementary Number Theory

Apr 7th, 2015

a^8 divides b^5 than b^5=ca^8

than b*b^4=c*a*a^7

therefore,

b/a=c*(a^7/b^4)

but a and b are positive integers,

so (a^7/b^4)=constant 

hence c*(a^7/b^4)=constant=d

hence proved

b=ad

therefore a divides b.

Apr 7th, 2015

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Apr 7th, 2015
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Apr 7th, 2015
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