Let n be any natural number such that 5^n-1 < 3ⁿ⁺¹. Then, the least integer value of m that satisfies 3ⁿ⁺¹ < 2^n+m for each such n, is

It is given that the inequality  holds when n is a natural number, specifically for n = 1, 2, 3, 4, and 5.

Now, we need to find the least integer value of m that satisfies the inequality 

For n=1, the least integer value of m is 2.

For n=2, the least integer value of m is 3.

For n=3, the least integer value of m is 4.

For n=4, the least integer value of m is 4.

For n=5, the least integer value of m is 5.

Hence, the least integer value of m such that for all the values of n, the equation holds is 5.