Q) Find the remainder when 7^23 is divided by 25 .

A) 7^23 = (7^22) . 7

= [ (7^2)^11] . 7

= [(50 - 1)^11] .7

Now In expansion of (50 - 1)^11 , all terms except the last one will be divisible by 25 since they contain an exponent of 50 in them.

Last term = 11C11 * (-1)

So we are left with

(-1)(7)

= -7

so 25 - 7 = 18 which is the remainder

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## Tuesday, September 16, 2008

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