solve using mathematical induction: 2 times 34^n -3 times 23^n +1 is divisible by 726 for all positive integers n.

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- Jun 26th 2012, 06:09 AMDoll0555Mathematical Induction :)
solve using mathematical induction: 2 times 34^n -3 times 23^n +1 is divisible by 726 for all positive integers n.

- Jun 26th 2012, 07:16 AMemakarovRe: Mathematical Induction :)
If , then , i.e., . Therefore,

.

So, it is sufficient to prove that is divisible by 22.