Forum - Arithmetics

Powers of natural numbers

Steve McLoud
Visitor
2015-12-09 12:47:22
#1
Find out the naturals n for which we have

23n+1 < (n+4)2

 

RE: Powers of natural numbers

SteveC
Member
2015-12-09 13:04:24
#2
This could be an answer.



For n=0
21 < 42 .... and this is true because 2 < 16

For n=1
24 < 52 ..... and this is true, as well, because 16 < 25

For n=2
27 < 62 .... but here it is not true anymore because 256 > 36

For n =3
210 < 72 ... neither here is not true

....

We can see that the first member increase faster then the second one so we won't have another solution.
so though: S={0, 1}
 
 

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