/sci/ - Science & Math

>>11709396
I misread.
Still, the solution posted is wrong, because the number of ways to choose not disjoint sets A, B from k elements is not [math]k(2^{k-1})^2[/math]. It is [math]4^k - 3^k[/math].
The correct answer to the problem is [math]5^n - 4^n[/math].

>>10407533
>>10407518
Since [math]\Phi_1, \dots \Phi_n[/math] are pairwise coprime, use CRT to solve the system
[math]N \equiv 0 \mod{\Phi_1}[/math]
[math]N \equiv -1 \mod{\Phi_2}[/math]
...
[math]N \equiv -n+1 \mod{\Phi_n}[/math]