Help please i can't find a solution to this

[old summit]

What do the three dots mean?

So you want to prove that $2^{12}$ is a factor of $3^{2^{10}}-1$?

[dire meadow]

SWR

[old summit]

Looks like an induction problem

[old summit]

So what have you tried?

[old summit]

!show

[wet ice]

Show your work, and if possible, explain where you are stuck.

[old summit]

Yeah I don't think that will help

Try to prove $2^k$ is a factor of $3^{2^k}-1$ using induction

[dire meadow]

SWR

[strong swallow]

Just factorise using difference of squares

And since all powers of 3 are odd

When you add one it becomes an even number

So you factor a 2 from each factor and the last factor is 8

So all the factors of 2 times 8 equals 2^12

[old summit]

!nosols

[wet ice]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.