Show that `3^(n) xx 4^(m)` cannot end with the digit 0 or 5 for any natural numbers ‘n’and 'm'

Check whether 6^n can end with the digit 0 for any natural number n.

Prove by mathematical induction that n^(5) and n have the same unit digit for any natural number n.

Prove that (n !+1) is not divisible by any natural number between 2 and n

Show that 1!+2!+3!++n ! cannot be a perfect square for any n in N ,ngeq4.

Using principle of mathematical induction, prove that 7^(4^(n)) -1 is divisible by 2^(2n+3) for any natural number n.

Use the principle of mathematical induction to show that 5^(2+1)+3^(n+2).2^(n-1) divisible by 19 for all natural number n.

Show that for a set of first n (le 2) natural number n < [n+1/2]^n

Which of one of the following is the domain of the relation R defined on the set NN of natural numbers are R= {(m,n): 2m + 3n =30 where m, n in NN} ?

Find the number of number between 300 and 3000 that can be formed with the digits 0,1,2,3,4 and 5, no digit being repeated in any number.

If S_(r ) be the sum of the cubes of first r natural numbers, then show that Sigma_(r=1)^(n) (2r+1)/(S_(r)) = (4n(n+2))/((n+1)^(2)) , for any natural number n.