Question

Show that 9^n can't end with 3 for any integer n.

Answer 1

Answer:

for any number to end with digit zero it mus have 2 and 5 in its prime factorisation. but 9^n can be prime factorised as 3^2n. since it does not have 5 in the prime factorisation by uniqueness  of the fundamental theorem of arithmetic 9^n cannot end with digit zero