$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?

Elevens

Age 16 to 18 Challenge Level:

Show that $3^{(3n+4)}+7^{(2n+1)}$ is a multiple of 11 for all
positive integer values of $n$.