Find the unit digit of the number (490497)252

Question

+7

1284

1

+413

Find the unit digit of the number (490497)²⁵²

kes1968 Aug 21, 2015

+33661

+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 490497²⁵² is 1

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Alan Aug 21, 2015

Alan · Answer 1 · 2015-08-21T08:24:57

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 490497²⁵² is 1

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