Need to be proved(Number Theory)

[Nika Losaberidze]

I need your help.
Prove that 11^n+2 + 12^2n+1 is divisible by 133 for all natural numbers n.
Thank you in advance

 

[Deleted member 4993]

I need your help.
Prove that 11^n+2 + 12^2n+1 is divisible by 133 for all natural numbers n.
Thank you in advance

Does your problem look like:

\(\displaystyle 11^n+2 + 12^2n+1\) .....OR.....

\(\displaystyle 11^{n+2} + 12^{2n+1}\)

......... or something else?​

​

Please use grouping symbols () or {} or [] to indicate order of operations.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[BigBeachBanana]

I need your help.
Prove that 11^n+2 + 12^2n+1 is divisible by 133 for all natural numbers n.
Thank you in advance

In either case, proof by induction is screaming out to you.

 

[AvgStudent]

Does your problem look like:

\(\displaystyle 11^n+2 + 12^2n+1\) .....OR.....

\(\displaystyle 11^{n+2} + 12^{2n+1}\)

......... or something else?​

​

Please use grouping symbols () or {} or [] to indicate order of operations.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

I think it must be the second case. Quick check for n = 1.
The first equation is [imath]11^1+2 + 12^2\times 1+1=158[/imath] and [imath]158/133[/imath] is irreducable.

The second equation is [imath]11^3+12^3=3059[/imath] and [imath]3059/133=23[/imath]

 

[Steven G]

Hint: 11^2 + 12 = 133