Difference between revisions of "2021 GMC 10B Problems/Problem 10"
(Created page with "==Problem== What is the remainder when <math>88!^{{{{(88!-1)}^{(88!-2)}}^{(88!-3)}}^{.....1}}\cdot 1^{2^{3^{4^{.....88!}}}}</math> is divided by <math>89</math>? <math>\textb...") |
m (→Solution) |
||
Line 7: | Line 7: | ||
Preface: there is a 89% chance this is wrong. | Preface: there is a 89% chance this is wrong. | ||
− | Note that by | + | Note that by [[Wilson's Theorem]], |
<cmath>88! \equiv -1 \pmod{89}.</cmath> | <cmath>88! \equiv -1 \pmod{89}.</cmath> | ||
Latest revision as of 19:35, 7 March 2022
Problem
What is the remainder when is divided by
?
Solution
Preface: there is a 89% chance this is wrong.
Note that by Wilson's Theorem,
We can substitute this in for to have
Note that the parity of is even. This means that
is odd. Since
is odd,
is consequently odd. Applying this to our congruence, we have
~pineconee