Question

What is the unit digit of (7^95-3^58)?

Answer 1

Cyclicity of 7:-

7,9,3,1,7,9....

Unit digits repeat after every 4th power of 7.

95/4= 23. Remainder=3. So unit digit of 7^95 is 3rd step of cyclicity i.e. 3

Cyclicity of 3:-

3, 9, 7,1, 3, 9....

Unit digits repeat after every 4th power of 3.

58/4= 19. Remainder = 2. So unit digit of 3^58 is 2nd step of cyclicity i.e 9.

9+ 3 = 12

But since e want the units digit we will consider only 2, which is the unit digit of given expression.

Hope this helps!