Question

units digit of 1^1*2^2*3^3......100^100 is zero?

Answer 1

what is the units digit of 100^100 ?

Answer 2

00000000

Answer 3

at leat no modolo here

Answer 4

well one 0 will do

Answer 5

modulo kicks in whenever you deal with remainders,
so modulo is there here also :)

Answer 6

oh but not necessary right

Answer 7

units digit = 1^1*2^2*3^3......100^100 mod 10
= (1^1*2^2*3^3......100^99)*10 mod 10
= (1^1*2^2*3^3......100^99)*0 mod 10
= 0 mod 10

Answer 8

depends on how much you love congruences ;)

Answer 9

gr8

Answer 10

a lil more challenging problem would be to find the units digit of SUM :

1^1 + 2^2 + 3^3+ ...... + 100^100

Answer 11

its 1

Answer 12

wow! how ?

Answer 13

1^1 just guessed

Answer 14

its opposit to mulitly

Answer 15

lol work it when free, it will be a nice practice for using congruences :)