Question

For any positive integer n, prove that 2^n * 3^n - 1 is always divisible by 17.

Answer 1

By using PMI

Answer 2

p(k) ..... p(1) ....... p(k+1)

Answer 3

can you expand please!

Answer 4

like the steps involved and such!

Answer 5

is it \[2^n 3^n -1\]or\[2^n(3^n-1)\]?

Answer 6

its the first one

Answer 7

Can u check ur question once more

Answer 8

but that statement is not true let n=1 or n=2 it gives 5 and 35 respectively but

5 not divides 17
35 not divides 17

Answer 9

Case I

the question should be wrong

Answer 10

CASE II

if the question is correct so...u can conclude that this statement does nt satify the condition

Answer 11

if i cant prove it, then i can prove that it cannot be proved by counterexamples.

Answer 12

does not satisfy the condition?

Answer 13

well try it by some arbitrary values for \(n\)

Answer 14

i mean for any value if n 2^n * 3^n - 1 is not divisible by 17.