#Numbers-8

What is the largest 2 digit value that N can take such that 88^N and 22 ^N have the same unit's digit?







Solution:-

 2 digit number : Range is from 10 to 99

 8 and 2 have a cyclicity of 4


Table for last digit when remainder 1,2,3,0

We get two options one with remainder 0 and one with remainder 2 whose last digits are same

Series :- 14 18 ........98(4a+2)...i.e remainder is 2
Series :- 12 16 ........96(4a)..ie. remainder is 0

 Hence the answer is 98(largest 2 digit value having the same unit digit

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