Prove a^(b^2) - a^(c^2) can be divided by a^b - a^c

Berrnie

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Oct 10, 2021
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If a,b,c are positive integers and b>c and a>1. Prove that ab2- ac2 can be divided by ab- ac

I tried to do something with binomial expansion formula but I didn’t come to anything helpful. I tried to make b dependent on c but it left me with more variables. So i am kinda lost and have no idea how to prove it 😞
 

Subhotosh Khan

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If a,b,c are positive integers and b>c and a>1. Prove that ab2- ac2 can be divided by ab- ac

I tried to do something with binomial expansion formula but I didn’t come to anything helpful. I tried to make b dependent on c but it left me with more variables. So i am kinda lost and have no idea how to prove it 😞
Rewrite the question using ab = x and ac=y

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 

Berrnie

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Oct 10, 2021
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Thank you for the tip <3
so ab=x and ac=y
so now we‘be got xb-yc and we have to prove it can be divided by x - y
I made b=c+k when k belongs to positive integers cause b>c and b,c belongs to positive integers
xc*xk - yc
i know we have to get to xc - yc so we can use formula xn-yn=(x-y)(xn-1+xn-2y+…+yn-1) and prove thesis
I know we have to somehow put xc - yc outside the brackets but I don’t know how
cause If you try to put this xk before the bracket you got xk(xc -(yc/xk))
any idea what should I do to get xc - yc?
 
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