Find the smallest natural number k such that `k(3^(3)+4^(3)+5^(3))=a^(b)` for some natural numbers a and b

0 is the smallest natural number.

Zero is the smallest natural number.

The smallest natural number is zero.

The smallest natural number is ....... .

Let a, b, c, d be real numbers such that sum_(k=1)^(n) (ak^(3) + bk^(2) + ck + d) = n^(4) or every natural number n. Then | a | + | b | + | C | + | d | is equal to

The smallest natural number is (a) 0 (b) 1 (c) -1 (d) None of these

If a,b,a and d are natural numbers such that a^(5)=b^(6),c^(3)=d^(4), and d-a=61, then the smallest value of c-b is :

A sequence b_(0),b_(1),b_(2), . . . is defined by letting b_(0)=5 and b_(k)=4+b_(k-1) , for all natural number k. Show that b_(n)=5+4n , for all natural number n using mathematical induction.

Find three smallest consecutive natural numbers such that the difference between one-third of the largest and one-fifth of the smallest is atleast 3 .