A number theory problem by Keerthi Reddy

The way to solve this problem is by applying congruence modulo First let me explain u congreunce modulo when an integer (a-b) is divisible by 'm' then we represent it in this way a=b(mod m).

In theses sort of problems we must only consider units place.. 2^20 As they are asking units digit we need to take m=10... if they ask Last two digits we need to take 100....... so as we know

2^5=2(mod 10) 2^5*4=2^4(mod 10) [Multiplying the powers by 4] 2^20=16(mod 10) Therefore 6 is the unit's digit

$242^{20}\equiv 2^{20}\equiv (2^4)^5\equiv 6^5\equiv \boxed{6} \pmod{10}$