It is proved that for every $n>1$ the arithmetical
operations $+$, $\times$ are definable in the structure
$\strN{B_n,f}$ where, $B_n(x,y)=\binom{x+y}x\MOD n$ and $f$
is one of the following functions: Euler function $\varphi$,
Carmichael function $\lambda$, the sum of divisor function
$\sigma$, the number of divisors function $\tau$, and the
prime counting function $\pi$. The same result is proved
also for the structure $\strN{+,\tau}$.
