Addition/Multiplication/Power/N/Injectivity/Exercise

Is the mapping

$\varphi \colon \mathbb {N} _{+}\times \mathbb {N} _{+}\longrightarrow \mathbb {N} _{+}\times \mathbb {N} _{+}\times \mathbb {N} _{+},(a,b)\longmapsto (a+b,ab,a^{b}),$

injective, or not?

Create a solution