Don't even think of expansion!

The number of integral terms in the expansion of ( 3 + 5 8 ) 256 (\sqrt{3} + \sqrt[8]{5})^{256} is


The answer is 33.

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1 solution

J C
Mar 29, 2016

You will only arrive at an integral term when the exponent is a multiple of 8, because you would be raising the 8th root to the 8th power, which makes an integer. From 0 to 256, there are 33 multiples of 8.

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