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**page929** Prove by induction the following:

10^(n+1) + 3*10^n + 5 is divisible by 9

I got the base step correct. Here is what I had for the inductive step:

Assume Pk is true, 9|10^(k+1) + 3*10^k + 5

Consider Pk+1

10^(k+2) + 3*10^(k+1) + 5

10(10^(k+1)) + 3*10^k(10) + 5

**At this point you should be seperating out....** $\displaystyle 10^{k+1}+(3)10^k+5$

**to get...** $\displaystyle 10\left(10^{k+1}+(3)10^k\right)+5=9\left(10^{k+1}+ (3)10^k\right)+10^{k+1}+(3)10^k+5$

(10^(k+1) + 3*10^k + 5) (10*10)

9|(10^(k+1) + 3*10^k + 5) (10*10) because 9|10^(k+1) + 3*10^k + 5

Any help would be greatful.