40. The sum of three consecutive odd numbers is equal to the fourth power of a single-digit number. Find all such triples of numbers.
40. The sum of three consecutive odd numbers is an odd number, and if the fourth power is an odd number, then the base is also odd. Therefore, single-digit numbers should be sought among the numbers $3,5,7,9$.
1) $(2 x-1)+(2 x+1)+(2 x+3)=3^{4}, 6 x+3=3^{4}$, from which $2 x+1=3^{3}$ and $x=$ $=13 ; 2 x-1=25 ; 2 x+1=27 ; 2 x+3=29 ; 25+27+29=81=3^{4}$;
2) $6 x+3=5^{4}$ (no integer solutions);
3) $6 x+3=7^{4}=2401$ (no integer solutions);
4) $6 x+3=9^{4} ; 2 x+1=2187 ; 2 x-1=2185 ; 2 x+3=2189$.

Thus, the problem has two solutions:

a) $25,27,29$; b) $2185,2187,2189$.