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exponents & powers

exponents & powers

by lokesh sardana -
Number of replies: 2
What will be the remainder when 2323 is devided by 53?
In reply to lokesh sardana

Re: exponents & powers

by Manish Verma -
This looks like an application of Binomial Theorem.

\(23^{23}=23 \times (529)^{11}\)
           =23 x (530-1)11
           = 23 x (53011-11C153010+11C25309- .....................-1)

There are 12 terms in the series out of which 11 are divisible by 53.

So, \(\frac{23^{23}}{53}=Int-\frac{23}{53}\)
Or, \(\frac{23^{23}}{53}=(Int-1)+1-\frac{23}{53}\)
\(\frac{23^{23}}{53}=+ve Int+\frac{30}{53}\)