1.

Find the last two digits of 3​

Answer»

ong>Step-by-step explanation:

This is same as asking what is REMAINDER when 3

1997

÷100

3

4

≡81mod100

3

8

≡61mod100

3

12

≡41mod100

3

16

≡21mod100

3

20

≡1mod100

Now, 3

40

,3

60

,3

80

,3

100

,....,3

1980

all are ≡1mod100

We know 3

16

≡21mod100

3

17

≡21×3mod100

3

17

≡63mod100

∴3

1997

≡3

1980

×3

17

since, 3

1980

≡1mod100

and 3

17

≡63mod100

∴3

1997

≡63mod100

∴ Last two digit is 63



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