What is the unit digit of 23 45 57 451 + 239 125 122 159 + 12345 + 412

SOLUTION

Cyclicity of 2,3 and 7 is 4

So in case of any number with unit digit 2,3 and 7 raised to some power, power is divided by 4 and remainder is obtained. We can find unit digit in this case using following table

Cyclicity of 9 is 2

Unit digit of numbers like (………9)ⁿ

i) when n is odd = 9

ii) when n is even = 1

So, 23⁴⁵57⁴⁵¹ + 239¹²⁵122¹⁵⁹ + 12345 + 4121

= 3  3 + 9  8 + 5 + 1 = 9+2+5+1 = 17