Bunuel wrote:
If n is the remainder when 2^50 is divided by 3 and m is the remainder when 2^15 is divided by 5, what is m + n?
A. 6
B. 5
C. 4
D. 3
E. 2
\(\frac{2^4}{3}\) = Remainder 1
So,\(2^{50} = 2^{4*12}*2^2\)
Now,\(\frac{2^2}{3}\) = Remainder 1
So, m =1
\(\frac{2^4}{5}\) = Remainder 1
So,\(2^{15} = 2^{4*3}*2^3\)
\(\frac{2^3}{5}\) = Remainder 3
So, n = 3
Hence,\(m + n = 1 + 3 = 4\)
Hence, Correct answer will be (C) 4
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