The remainder of (3)67! divided by 80 is :
B. 1
C. 2
D. 3
E. 4
Answer: Option B
Solution (By Examveda Team)
Since, $${3^4} = 81$$ gives remainder 1 on divided by 80So, $$\frac{{{3^{4n}}}}{{80}}$$ gives remainder 1
Thus, $$\frac{{{3^{67!}}}}{{80}}$$ will also give the remainder as 1
Since, 67! = 4n for a positive integer n
This Question Belongs to Arithmetic Ability >> Number System
We always have, 3^4 = 81 == 1 mod 80. Hence, for any positive integer n, we have, 3^(4^n )=1 mod n. Hence, the answer is option B.
By Sanjay Mohan Bhatnagar (www.mathsacad99.com)