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Number Theory Level 3

Find the remainder when $\huge 35^{55^{88}}$ Is divided by 6.

2 6 4 1 5 3

1 solution

Ryan Tamburrino
Jul 31, 2015

Clearly, $35\equiv -1 \mod{6}$ , so the three-story-power-tower in question can be reduced to $35^{{55}^{88}} \equiv (-1)^{{55}^{88}} \mod{6}$ Now $55^{88}$ is clearly an odd number. So we can say $(-1)^{{55}^{88}} = -1 \equiv 5 \mod{6}$

Very clear and nice solution.upvoted .

abhigyan adarsh - 5 years, 10 months ago

The $\LaTeX$ in the question needs to be fixed.

The fixed (and easier to read) version is: $\huge 35^{55^{88}}$ .

The $\LaTeX$ code to write that can be seen by hovering your mouse cursor over the rendered output in my comment. Please edit your question accordingly so that others can read your question properly.

Prasun Biswas - 5 years, 10 months ago

thanks for the latex

abhigyan adarsh - 5 years, 10 months ago

$\large 35^{55^{88}}$ The question misplaces the second } which should be the last .

Niranjan Khanderia - 5 years, 10 months ago

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