#1**+15 **

A little experimentation shows that the successive powers of 490497 end in 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, .... etc.

So if the remainder of the power, when divided by 4 is zero the result ends in 1, if the remainder is 1 the result ends in 7, etc.

Now, mod(252,4) = 0, so the units digit of 490497^{252} is 1

.

Alan
Aug 21, 2015

#1**+15 **

Best Answer

A little experimentation shows that the successive powers of 490497 end in 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, .... etc.

So if the remainder of the power, when divided by 4 is zero the result ends in 1, if the remainder is 1 the result ends in 7, etc.

Now, mod(252,4) = 0, so the units digit of 490497^{252} is 1

.

Alan
Aug 21, 2015