Question

Show that 3power n x4power m cannot end with the digit 0or5 for any natural number n and m

Answer 1

For a number to end with 0 or 5 it's factorisation must contain the digits 2 and 5 . But since 3n and 4n i.e. 2x2n , Doesn't contain 5 and 2 in their factorisation.
T herefore they don't end with a zero or 5