let f(n)=52n−23n=25n−8nf(1)=25−8=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+1−8n+1=25⋅25n−8⋅8n=25⋅25n−25⋅8n+17⋅8n=25(25n−8n)+17⋅8n=25⋅17m+17⋅8n,( f(n) =17m by assumption)17(25m+8n)and this is clearly divisible by 17
.let f(n)=52n−23n=25n−8nf(1)=25−8=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+1−8n+1=25⋅25n−8⋅8n=25⋅25n−25⋅8n+17⋅8n=25(25n−8n)+17⋅8n=25⋅17m+17⋅8n,( f(n) =17m by assumption)17(25m+8n)and this is clearly divisible by 17