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sHOW THAT 5^2n -2^3n is divisible by 17

 Sep 29, 2018

Best Answer 

 #1
avatar+6252 
+3

let f(n)=52n23n=25n8nf(1)=258=17 which is clearly divisible by 17

 

Now assume that f(n) is divisible by 17. We need to show that f(n+1) is as wellf(n+1)=25n+18n+1=2525n88n=2525n258n+178n=25(25n8n)+178n=2517m+178n,( f(n) =17m by assumption)17(25m+8n)and this is clearly divisible by 17

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 Sep 29, 2018
 #1
avatar+6252 
+3
Best Answer

let f(n)=52n23n=25n8nf(1)=258=17 which is clearly divisible by 17

 

Now assume that f(n) is divisible by 17. We need to show that f(n+1) is as wellf(n+1)=25n+18n+1=2525n88n=2525n258n+178n=25(25n8n)+178n=2517m+178n,( f(n) =17m by assumption)17(25m+8n)and this is clearly divisible by 17

Rom Sep 29, 2018

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